Mathematics
Formal structures, relations, transformations, and deductive consequences.
Fields and domains
Physics
Empirical theories and models of matter, energy, spacetime, interactions, and physical systems.
Chemistry
Composition, structure, properties, measurement, and transformations of substances across molecular, material, biological, environmental, and industrial scales.
- Chemical foundations
- Atomic structure & periodicity
- Molecular structure & bonding
- Quantum chemistry & spectroscopy
- Chemical thermodynamics & equilibrium
- Solutions, acids, bases & interfaces
- Chemical kinetics & dynamics
- Inorganic & coordination chemistry
- Organic chemistry
- Analytical chemistry
- Electrochemistry
- Radiochemistry
- Chemical experiments & evidence
Relation legend: 25 active meanings
Add data
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
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Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
Induced / forgotten
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
Canonical construction
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
Quotient construction
Identify elements by a stated equivalence relation and equip the quotient with the induced structure. The edge detail must state the representatives and equivalence relation.
Canonical embedding
Map one structure injectively into another by the standard structure-preserving inclusion or representation. This records a canonical copy, not necessarily literal set containment.
Combine compatible structures
Feed several structures into a construction junction and impose compatibility between them.
Representation / equivalence
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
Theorem implication
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
Mathematical formulation
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
Framework specialization
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
Quantization
A classical system or field theory is used to construct a quantum theory through a stated quantization procedure. Quantization need not be unique and is not guaranteed to preserve every classical structure.
Theory component
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
Describes / governs
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
Physical constitution / realization
The source is a material constituent, structural component, or underlying quantum field whose excitation realizes the target physical system or particle. The edge label and detail must distinguish composition from field excitation; neither implies a simple classical sum of parts.
Classification
The target is a member or subtype of the broader source class.
Physical interaction / binding
The source field, particle, charge, current, or interaction couples to, acts on, binds, forms, or stabilizes the target in the stated regime. The edge label and detail must identify the exact coupling, interaction, or binding claim and its qualifications.
Limit / controlled approximation
The target is recovered from the source either in a stated mathematical or asymptotic limit, or through a quantitatively controlled approximation with identified small parameters or omitted terms. The edge label and detail must state which case applies and its regime of validity.
Effective theory / model
The target retains the degrees of freedom and interactions relevant below a stated scale or within a stated regime, while higher-energy or unresolved degrees of freedom from the source are integrated out, coarse-grained, or encoded in effective couplings.
Model / approximation method
The target is a model, idealization, restricted ansatz, approximation scheme, phenomenological fit, or historical representation used for the source system or theory. It need not have a universal small error parameter and is not thereby a controlled limit or effective theory. The edge label and detail must identify the precise status.
Emergent / collective behavior
The target is a collective, organizational, or scale-dependent phenomenon of the source constituents and interactions; it is not a mere list or classical sum of constituents.
State / property description
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
Transformation / process
A physical process transforms the source into, or produces, the target under the conditions stated in the edge detail.
Historically motivated
The source experiment, observation, anomaly, or problem materially motivated the development, revision, or acceptance of the target concept. Historical influence is not logical derivation; the edge detail states the documented role and avoids retrospective origin myths.
Experimentally tested / supported by
The source theory, law, entity, prediction, or structural claim is directly tested, supported, constrained, or established by the target experiment or observation. Experimental support is not final logical proof; the edge detail states exactly what was measured.
Browse all 1,330 canonical concepts
These are ordinary HTML links to the canonical concept pages. Construction junctions remain visible in the diagram but are omitted here because they are visual combination devices rather than standalone concepts.
Mathematics
Set theory45
- Aleph hierarchy
- Axiom of choice (AC)
- Beth hierarchy
- Cantor’s theorem
- Cardinal
- Cardinality of the continuum
- Class of all ordinals
- Continuum hypothesis
- Countable infinity
- Countable ordinal
- Countable set
- Cumulative hierarchy
- Empty set
- Epsilon-zero ordinal
- Finite cardinal
- Finite ordinal
- Finite set
- First infinite ordinal
- First uncountable ordinal
- Function
- Generalized continuum hypothesis
- Indexed family
- Infinite cardinal
- Large cardinal
- Limit cardinal
- Limit ordinal
- Measurable cardinal
- Ordinal
- Ordinal arithmetic
- Pointed set
- Power set
- Set
- Strongly inaccessible cardinal
- Successor cardinal
- Successor ordinal
- Supercompact cardinal
- Transfinite recursion
- Transitive set
- Von Neumann one
- Von Neumann successor
- Von Neumann zero
- Well-founded relation
- Well-ordering theorem
- Zermelo–Fraenkel set theory (ZF)
- Zermelo–Fraenkel set theory with Choice (ZFC)
Order theory28
- Binary relation
- Boolean algebra
- Bounded distributive lattice
- Bounded lattice
- Bounded poset
- Complete Boolean algebra
- Complete lattice
- Directed set
- Directed-complete partial order
- Distributive lattice
- Equivalence relation
- Frame / complete Heyting algebra
- Galois connection
- Heyting algebra
- Join-semilattice
- Lattice
- Lattice-ordered group
- Meet-semilattice
- Monotone map
- Ordered field
- Ordered ring
- Partial order / poset
- Pointed CPO
- Preorder
- Residuated lattice
- Total order
- Totally ordered group
- Well-order
Logic17
- Compactness theorem
- Consistent formal theory
- First-order signature
- First-order structure
- First-order theory
- Formal proof system
- Gödel completeness theorem
- Gödel’s first incompleteness theorem
- Gödel’s second incompleteness theorem
- Hilbert’s program
- Modal Kripke model
- Model of a theory
- Normal modal algebra
- Propositional intuitionistic Kripke model
- Satisfaction relation
- Semantic consequence
- Syntactically complete formal theory
Computability theory12
Category theory29
- Abelian category
- Additive category
- Adjunction
- Braided monoidal category
- Cartesian category
- Cartesian closed category
- Categorical colimit
- Categorical limit
- Category
- Closed monoidal category
- Compact closed category
- Cosimplicial object
- Dagger category
- Elementary topos
- Enriched category
- Finitely complete category
- Functor
- Grothendieck topos
- Groupoid
- Monoidal category
- Natural transformation
- Preadditive category
- Presheaf
- Representable presheaf
- Simplicial object
- Site
- Small category
- Symmetric monoidal category
- Thin category
Combinatorics & graph theory18
Universal algebra8
Algebra53
- *-algebra
- Abelian group
- Affine space
- Algebra over a field
- Algebraic field extension
- Algebraically closed field
- Associative algebra
- Bialgebra
- Clifford algebra
- Coalgebra
- Commutative monoid
- Commutative ring
- Commutative unital algebra over a field
- Complex vector space
- Direct sum of vector spaces
- Division ring
- Dual vector space
- Exterior algebra
- Field
- Field automorphism
- Field extension
- Fixed field
- Fundamental theorem of Galois theory
- Galois extension
- Galois group
- Gamma matrices
- Grassmann algebra
- Group
- Hopf algebra
- Ideal
- Lie algebra
- Magma
- Module over a ring
- Monoid
- Normal field extension
- Operator anticommutator
- Operator commutator
- Perfect field
- Polynomial ring
- Quadratic form
- Quotient ring
- Ring
- Semigroup
- Semiring
- Separable field extension
- Slater determinant
- Solvability by radicals
- Solvable group
- Splitting field
- Symplectic vector space
- Tensor-product vector space
- Unital associative algebra
- Vector space
Representation theory14
Number theory35
- Adele ring
- Complete valued field
- Completion at a valuation
- Dedekind domain
- Difference pairs of natural numbers
- Discrete valuation ring
- Euclidean domain
- Everywhere locally soluble variety
- Finite field
- GCD domain
- Global field
- Hasse–Minkowski theorem
- Integer fraction pairs
- Integers
- Integral domain
- Local field
- Local point
- Local–global principle
- Natural numbers
- Number field
- -adic field
- Peano system
- Place of a number field
- Prime ideal
- Principal ideal domain
- Rational numbers
- Real closed field
- Residue field
- Ring of integers
- Successor structure
- Unique factorization domain
- Valuation
- Valuation ring
- Valued field
- Variety violating the Hasse principle
Algebraic geometry27
- Affine scheme
- Algebraic space
- Algebraic variety
- Artinian ring
- Complete local ring
- Integral scheme
- Local ring
- Localization of a commutative ring
- Locally ringed space
- Morphism of schemes
- Noetherian ring
- Noetherian scheme
- Prime spectrum
- Projective scheme
- Rational point
- Reduced scheme
- Regular local ring
- Regular scheme
- Ringed space
- Scheme
- Scheme over a base
- Separated scheme
- Sheaf
- Sheaf of groups
- Sheaf of rings
- Smooth projective quadric
- Stalk of a sheaf
Topology36
- Compact Hausdorff space
- Compact metric space
- Compact space
- Complete metric space
- Connected space
- Continuous map
- Fiber bundle
- First-countable space
- Hausdorff space
- Homeomorphism
- Locale
- Locally compact Hausdorff space
- Locally compact space
- Locally connected space
- Locally Euclidean space
- Metric space
- Normal space
- Polish space
- Pseudometric space
- Quotient space
- Regular space
- Second-countable space
- Separable metric space
- space
- space
- Topological field
- Topological group
- Topological manifold
- Topological monoid
- Topological ring
- Topological semigroup
- Topological space
- Totally disconnected space
- Tychonoff space
- Uniform space
- Zero-dimensional space
Algebraic topology21
- Cohomology group
- Cohomology ring
- Compactly generated space
- Contractible space
- Covering space
- CW complex
- Fundamental group
- -space
- Higher homotopy group
- Homology group
- Homotopy
- Homotopy equivalence
- Homotopy type
- Loop space
- Path-connected space
- Pointed topological space
- Simplicial set
- Simply connected space
- Singular chain complex
- Singular cochain complex
- Topological pair
Differential geometry41
- Compact Lie group
- Complex manifold
- Connection on a vector bundle
- Contact manifold
- Cotangent bundle
- Curvature form
- de Rham complex
- Differential form
- Einstein tensor
- Exterior derivative
- Foliated manifold
- Geodesic
- Hermitian manifold
- Hodge star operator
- Kähler manifold
- Levi–Civita connection
- Lie group
- Lie groupoid
- Lorentzian manifold
- Manifold with affine connection
- Oriented smooth manifold
- Poisson manifold
- Principal bundle
- Principal connection
- Pseudo-Riemannian manifold
- Real-analytic manifold
- Ricci curvature tensor
- Riemann curvature tensor
- Riemannian manifold
- Scalar curvature
- Smooth curve
- Smooth manifold
- Smooth manifold with boundary
- Smooth vector bundle
- Spin structure
- Symplectic manifold
- Tangent bundle
- Tangent vector
- Tensor bundle
- Tensor field
- Vector bundle
Homological algebra21
- Bigraded object
- Chain complex
- Chain map
- Cochain complex
- Derived category
- DG-category
- Differential graded algebra
- Double complex
- Exact category
- Exact sequence
- Ext functor
- Graded object
- Grothendieck abelian category
- Injective module
- Long exact sequence
- Mapping cone
- Model category
- Projective module
- Quasi-isomorphism
- Tor functor
- Triangulated category
Analysis51
- Adjoint operator
- Banach algebra
- Banach space
- Bosonic Fock space
- Bounded linear operator
- -algebra
- Calculus of variations
- Cauchy sequences of rationals
- Complex numbers
- Dedekind-cut real line
- Densely defined operator
- Derivative
- Differentiable function
- Differential operator
- Fermionic Fock space
- Fock space
- Fourier transform
- Fréchet space
- Functional derivative
- Green function
- Hilbert space
- Inner-product space
- Laplace operator
- Lebesgue integral
- Linear operator
- Locally convex space
- Normed vector space
- Operator spectrum
- Ordered-pair complex field
- Ordinary differential equation
- Partial differential equation
- Partial trace
- Polynomial-quotient complex field
- Positive operator
- Projection operator
- Projective Hilbert space
- Real numbers
- Rigged Hilbert space
- Schwartz space
- Self-adjoint operator
- Seminormed vector space
- Sobolev space
- Space of distributions
- Spectral measure
- Spectral theorem for self-adjoint operators
- Spherical harmonic
- Stone theorem
- Tensor-product Hilbert space
- Topological vector space
- Trace-class operator
- Unitary operator
Dynamical systems20
- Attractor
- Bifurcation
- Chaotic dynamics
- Continuous-time dynamical system
- Discrete-time dynamical system
- Dynamical stability
- Dynamical system
- Ergodic dynamical system
- Fixed point of a dynamical system
- Hamiltonian dynamical system
- Invariant set
- Lyapunov exponent
- Lyapunov stability
- Measure-preserving dynamical system
- Orbit / trajectory
- Parameterized dynamical system
- Periodic orbit
- Poincaré return map
- Self-map
- Smooth flow
Probability15
- Central limit theorem
- Conditional expectation
- Conditional probability
- Convergence in probability
- Expected value
- Filtered probability space
- Filtration
- Independent random variables
- Law of large numbers
- Markov chain
- Normal distribution
- Probability distribution
- Random variable
- Standard probability space
- Stochastic process
Measure10
Physics
Physical foundations20
- Binding energy
- Conservation law
- Continuity equation
- Coupling constant
- Degree of freedom
- Dimensional analysis
- Effective description
- Energy
- Equation of motion
- Fundamental interaction
- Observable
- Physical dimension
- Physical law
- Physical model
- Physical quantity
- Physical scale
- Physical state
- Physical symmetry
- Physical system
- Physical theory
Classical mechanics21
- Action functional
- Canonical momentum
- Classical field theory
- Classical mechanics
- Classical point particle
- Configuration space
- Euler–Lagrange equation
- Force
- Galileo’s inclined-plane experiments
- Hamiltonian
- Hamiltonian mechanics
- Lagrangian
- Lagrangian density
- Lagrangian mechanics
- Linear momentum
- Newton’s laws of motion
- Newtonian mechanics
- Phase space
- Poisson bracket
- Rigid-body dynamics
- Stationary-action principle
Relativity & gravitation46
- 1919 eclipse light-deflection observations
- Binary black-hole system
- Black hole
- Causal structure
- Cavendish torsion-balance experiment
- Einstein field equation
- Energy–momentum four-vector
- Eötvös torsion-balance experiments
- Equivalence principle
- Event horizon
- Fizeau moving-water experiment
- Four-vector
- Four-velocity
- General relativity
- Geodesic motion
- Gravitation
- Gravitational collapse
- Gravitational lensing
- Gravitational wave
- GW150914 gravitational-wave detection
- Hawking radiation
- Hulse–Taylor binary-pulsar observations
- Inertial frame
- Ives–Stilwell experiment
- Kennedy–Thorndike experiment
- Kerr spacetime
- Light cone
- Lorentz symmetry
- Mass–energy equivalence
- Mercury perihelion anomaly
- Michelson–Morley experiment
- Minkowski spacetime
- Newtonian gravitation
- Physical event
- Poincaré symmetry
- Pound–Rebka experiment
- Proper time
- Relativistic particle mechanics
- Schwarzschild spacetime
- Shapiro time-delay measurement
- Spacetime
- Spacetime metric
- Special relativity
- Stress–energy tensor
- Weak-field gravity
- Worldline
Cosmology13
Electromagnetism19
- Classical electromagnetism
- Coulomb law
- Coulomb potential
- Electric field
- Electric four-current
- Electromagnetic field
- Electromagnetic four-potential
- Electromagnetic radiation
- Electromagnetic wave
- Electrostatics
- Faraday’s induction experiments
- Fine-structure constant
- Hertz electromagnetic-wave experiments
- Lorentz force law
- Magnetic field
- Maxwell equations
- Ørsted’s compass experiment
- Poynting vector
- Young’s double-slit experiment
Quantum mechanics61
- Aharonov–Bohm interference experiments
- Annihilation operator
- Anomalous Zeeman-effect observations
- Bell theorem
- Bell-test experiments
- Blackbody spectrum and ultraviolet catastrophe
- Born rule
- Bose–Einstein statistics
- Canonical commutation relations
- Cavity-QED decoherence experiments
- Compton scattering experiment
- Creation operator
- Davisson–Germer electron-diffraction experiment
- Density operator
- Dirac equation
- Einstein–Podolsky–Rosen argument
- Excited state
- Fermi–Dirac statistics
- Fullerene matter-wave interference
- Ground state
- Hong–Ou–Mandel experiment
- Identical quantum particles
- Klein–Gordon equation
- Many-body quantum mechanics
- Mixed quantum state
- Nonrelativistic quantum mechanics
- Occupation-number state
- Orbital angular momentum
- Parity
- Pauli equation
- Pauli exclusion principle
- Photoelectric-effect experiments
- Pure quantum state
- Quantum angular momentum
- Quantum bound state
- Quantum decoherence
- Quantum entanglement
- Quantum expectation value
- Quantum harmonic oscillator
- Quantum measurement
- Quantum mechanics
- Quantum number
- Quantum observable
- Quantum perturbation theory
- Quantum scattering theory
- Quantum state
- Quantum superposition
- Quantum system
- Quantum tunneling
- Quantum variational method
- Relativistic wave equations
- Scattering state
- Schrödinger equation
- Second-quantized formalism
- Single-particle double-slit experiments
- Spin
- Spin one-half
- Stern–Gerlach experiment
- Uncertainty principle
- Unitary time evolution
- Wavefunction
Thermodynamics & statistical mechanics33
- Boltzmann distribution
- Boltzmann entropy
- Canonical ensemble
- Classical statistical mechanics
- Critical phenomena
- Equilibrium thermodynamics
- Ergodic hypothesis
- First law of thermodynamics
- Fluctuation–dissipation theorem
- Gibbs entropy
- Grand-canonical ensemble
- Heat capacity
- Helmholtz free energy
- Macrostate space
- Microcanonical ensemble
- Microstate space
- Nonequilibrium statistical mechanics
- Order parameter
- Phase transition
- Quantum statistical mechanics
- Second law of thermodynamics
- Statistical ensemble
- Statistical mechanics
- Statistical partition function
- Temperature
- Thermodynamic entropy
- Thermodynamic equilibrium
- Thermodynamic limit
- Thermodynamic state
- Thermodynamic state variable
- Thermodynamic system
- Universality class
- Zeroth law of thermodynamics
Quantum field theory109
- Abelian gauge theory
- Approximate chiral symmetry of QCD
- Asymptotic freedom
- Bosonic quantum field
- Brout–Englert–Higgs mechanism
- BRST symmetry
- Canonical field quantization
- Casimir-force measurements
- Charge conjugation
- Charged fields
- Chiral perturbation theory
- Conserved charge
- Correlation function
- CPT theorem
- Effective field theory
- Electron anomalous-magnetic-moment measurements
- Electroweak gauge-boson self-interaction
- Electroweak gauge-field mixing
- Electroweak symmetry breaking
- Electroweak theory
- Faddeev–Popov ghost field
- Fermi theory of weak interactions
- Fermionic quantum field
- Feynman diagram
- Four-fermion interaction
- Free quantum field
- Gauge field
- Gauge field strength
- Gauge field theory
- Gauge fixing
- Gauge interaction
- Gauge redundancy
- Gauge-anomaly cancellation
- Gauge-covariant derivative
- Global physical symmetry
- Gluon gauge field
- Gluon self-interaction
- Goldstone theorem
- Higgs doublet field
- Higgs field
- Higgs vacuum expectation value
- Higgs–gauge interaction
- Interacting quantum field
- Lattice QCD
- Left-handed fermion field
- Left-handed lepton doublet field
- Left-handed quark doublet field
- Lepton field
- Local gauge invariance
- Locality principle
- Longitudinal massive-gauge-boson mode
- Low-energy effective field theory below the electroweak scale (LEFT)
- Low-energy QCD
- Matter field
- Microcausality
- Multiparticle state
- Nambu–Goldstone mode
- Noether current
- Noether theorem
- Non-Abelian gauge theory
- One-particle state
- Operator-valued distribution
- Path-integral formulation
- Perturbative quantum field theory
- Photon field
- Photon–fermion interaction
- Propagator
- Pseudo-Nambu–Goldstone mode
- Quantum anomaly
- Quantum chromodynamics
- Quantum electrodynamics
- Quantum field
- Quantum field operator
- Quantum field theory
- Quark condensate
- Quark field
- Quark–gluon interaction
- Regularization
- Renormalization
- Renormalization group
- Right-handed charged-lepton field
- Right-handed down-type quark field
- Right-handed fermion field
- Right-handed up-type quark field
- Running coupling
- -matrix
- Scalar field
- Scalar self-interaction
- Scattering amplitude
- Spin–statistics theorem
- Spinor field
- Spontaneous chiral-symmetry breaking in QCD
- Spontaneous symmetry breaking
- Standard Model chiral fermion multiplet
- Standard Model effective field theory
- Standard Model fermion field
- Standard Model gauge group
- Standard Model Lagrangian
- Vacuum state
- Vector field in physics
- Ward–Takahashi identity
- Weak-hypercharge gauge field
- Weak-isospin gauge fields
- Wilsonian effective action
- Would-be Goldstone mode
- Yang–Mills mass gap
- Yang–Mills theory
- Yukawa interaction
- field
Particle physics96
- Antineutrino
- Antiparticle
- Antiquark
- ATLAS and CMS Higgs-boson discovery
- Baryon
- Baryon number
- Boson
- Bottom quark
- Brookhaven muon-neutrino experiment
- Charged lepton
- Charged-current weak interaction
- Charm quark
- Chirality
- CKM matrix
- Color charge
- Color confinement
- Color-singlet state
- Composite particle
- Constituent-quark model
- Cowan–Reines reactor-neutrino experiment
- CP violation
- Down quark
- Electric charge
- Electromagnetic interaction
- Electron
- Electron antineutrino
- Electron neutrino
- Elementary particle
- Fermion
- Fermion generation
- First fermion generation
- Flavor
- Gargamelle neutral-current discovery
- Gauge boson
- Gluon
- Goldhaber neutrino-helicity experiment
- Hadron
- Hadronization
- Helicity
- Higgs boson
- Isospin
- discovery and the November Revolution
- Kaon CP-violation experiment
- LEP precision electroweak measurements
- Lepton
- Lepton number
- Meson
- Millikan oil-drop experiment
- Muon
- Muon antineutrino
- Muon discovery in cosmic rays
- Muon neutrino
- Neutral-current weak interaction
- Neutrino
- Neutrino flavor state
- Neutrino mass
- Neutrino mass eigenstate
- Neutrino mixing
- Neutrino oscillation
- Particle mass
- Particle or field polarization
- PETRA three-jet gluon evidence
- Photon
- PMNS matrix
- Positron
- Positron discovery in cloud-chamber tracks
- Quark
- Quark flavor mixing
- Sea-quark degrees of freedom
- Second fermion generation
- SLAC deep-inelastic scattering experiments
- SNO solar-neutrino flavor-change measurement
- Solar-neutrino deficit
- Standard Model of particle physics
- Strange quark
- Strong interaction
- Super-Kamiokande atmospheric-neutrino result
- Tau antineutrino
- Tau lepton
- Tau neutrino
- Tau-lepton discovery
- Third fermion generation
- Thomson cathode-ray experiments
- Top quark
- Top-quark discovery at the Tevatron
- UA1 and UA2 discovery of the and bosons
- Up quark
- Upsilon and bottom-quark discovery
- Valence-quark content
- boson
- Weak hypercharge
- Weak interaction
- Weak isospin
- Weak mixing angle
- Wu parity experiment
- boson
Nuclear physics51
- Alpha decay
- Alpha particle
- Antineutron
- Antiproton
- Aston mass-spectrograph measurements
- Atomic nucleus
- Beta decay
- Beta-minus decay
- Beta-plus decay
- Chadwick neutron experiment
- Continuous beta-spectrum problem
- Deuteron
- Electron capture
- Gamma decay
- Geiger–Marsden gold-foil experiment
- Isotone
- Isotope
- Liquid-drop model
- Mass number
- Neutron
- Neutron capture
- Neutron number
- Nuclear binding energy
- Nuclear Coulomb interaction
- Nuclear effective field theory
- Nuclear energy level
- Nuclear fission
- Nuclear force
- Nuclear fusion
- Nuclear isobar
- Nuclear isomer
- Nuclear magic-number systematics
- Nuclear many-body system
- Nuclear mass defect
- Nuclear mean-field theory
- Nuclear potential
- Nuclear shell model
- Nuclear spin
- Nuclear state
- Nucleon
- Nucleon–nucleon interaction
- Nuclide
- One-pion exchange
- Pion
- Pion discovery in nuclear emulsions
- Proton
- Proton number
- Radioactive decay
- Residual strong interaction
- Rutherford proton-transmutation experiment
- Three-nucleon force
Atomic & molecular physics70
- Atom
- Atomic absorption
- Atomic energy level
- Atomic fine structure
- Atomic Hamiltonian
- Atomic hyperfine structure
- Atomic ionization
- Atomic isotope shift
- Atomic orbital
- Atomic QED corrections
- Atomic selection rule
- Atomic spectrum
- Atomic state
- Atomic term symbol
- Atomic transition
- Balmer hydrogen-spectrum observations
- Bohr model
- Bound-electron self-energy
- Breit interaction
- Center-of-mass separation
- Central-field approximation
- Configuration-state function
- Darwin term
- Density-functional theory
- Dirac–Coulomb Hamiltonian
- Electric-dipole transition
- Electromagnetic atomic binding
- Electron correlation
- Electron shell
- Electron subshell
- Electron–electron Coulomb interaction
- Electron–nucleus Coulomb interaction
- Electronic screening
- Exchange interaction
- Finite nuclear-size effect
- Franck–Hertz experiment
- Hartree method
- Hydrogen atom
- Hydrogen-like ion
- Independent-particle model
- Infinite-nuclear-mass approximation
- jj coupling
- Lamb shift
- Lamb–Retherford experiment
- LS coupling
- Magnetic quantum number
- Many-electron atom
- Moseley X-ray spectroscopy
- Nonrelativistic Coulomb Hamiltonian
- Nonrelativistic QED
- Nuclear recoil correction
- One-electron atomic system
- Orbital angular-momentum quantum number
- Perrin Brownian-motion experiments
- Photoionization
- Principal quantum number
- Proton-radius puzzle
- Reduced-mass treatment
- Relativistic atomic structure
- Relativistic kinetic-energy correction
- Rutherford nuclear atom model
- Rydberg formula
- Spin-projection quantum number
- Spin–orbit coupling
- Spontaneous emission
- Stark effect
- Stimulated emission
- Total angular-momentum quantum number
- Vacuum polarization
- Zeeman effect
Condensed-matter physics31
- Band insulator
- Band metal
- BCS theory
- Bloch state
- Bloch theorem
- Collective excitation
- Condensed-matter physics
- Conventional superconductivity
- Cooper pair
- Crystal lattice model
- Crystalline solid
- Electronic band structure
- Electronic condensed-matter system
- Fermi surface
- Fermi-liquid theory
- Ferromagnetism
- Hubbard model
- Ising model
- Lattice vibration
- Magnetic order
- Nearly-free-electron model
- Periodic-electron model
- Phonon
- Quantum Hall effect
- Quantum many-body system
- Quasiparticle
- Reciprocal lattice
- Semiconductor
- Superconductivity
- Tight-binding model
- Two-dimensional electron gas
Experiments & observations3
Chemistry
Chemical foundations24
- Amount of substance
- Anion
- Cation
- Chemical compound
- Chemical equation
- Chemical formula
- Chemical mixture
- Chemical species
- Chemical substance
- Empirical formula
- Ion
- Lavoisier’s quantitative combustion program
- Law of definite proportions
- Law of multiple proportions
- Limiting reactant
- Mass conservation in chemical reactions
- Matter in chemistry
- Molar mass
- Mole
- Molecular formula
- Molecule
- Proust’s compound-composition measurements
- Pure substance
- Stoichiometry
Atomic structure & periodicity18
- Atomic-radius trend
- Chemical element
- Chemical valence
- Effective nuclear charge
- Electron affinity
- Electron configuration
- Electronegativity
- Gallium discovery and periodic prediction test
- Ionization energy
- Mendeleev’s periodic predictions
- Oxidation state
- Periodic law
- Periodic table
- Periodic trend
- Periodic-table block
- Periodic-table group
- Periodic-table period
- Valence electron
Molecular structure & bonding21
- Bond order
- Chemical bond
- Covalent bond
- Formal charge
- Hydrogen bond
- Intermolecular interaction
- Ionic bonding
- Lewis structure
- Molecular conformation
- Molecular dipole moment
- Molecular geometry
- Molecular graph
- Molecular structure
- Molecular symmetry
- Molecular-orbital theory
- Orbital hybridization
- Pi bond
- Resonance in chemical structure
- Sigma bond
- Valence-bond theory
- VSEPR model
Quantum chemistry & spectroscopy21
- Ab initio quantum chemistry
- Basis set
- Beer–Lambert law
- Bloch–Purcell nuclear-induction experiments
- Born–Oppenheimer approximation
- Configuration interaction
- Coupled-cluster method
- Electronic-structure calculation
- Hartree–Fock method
- Infrared spectroscopy
- Molecular rotation
- Molecular spectroscopy
- Molecular vibration
- Nuclear magnetic resonance spectroscopy
- Potential-energy surface
- Quantum chemistry
- Raman spectroscopy
- Raman’s inelastic-scattering observations
- Rotational spectroscopy
- Ultraviolet–visible spectroscopy
- Vibrational spectroscopy
Chemical thermodynamics & equilibrium18
- Calorimetry
- Chemical equilibrium
- Chemical phase diagram
- Chemical potential
- Chemical standard state
- Chemical thermodynamics
- Enthalpy
- Equilibrium constant
- Gibbs energy
- Gibbs phase rule
- Guldberg–Waage reaction studies
- Hess’s law
- Hess’s thermochemical measurements
- Law of mass action
- Le Chatelier’s principle
- Reaction enthalpy
- Reaction quotient
- Standard reaction Gibbs energy
Solutions, acids, bases & interfaces35
- Acid dissociation constant
- Acid–base equilibrium
- Activity coefficient
- Adsorption
- Adsorption isotherm
- Amphoterism
- Arrhenius’s electrolyte-conductivity studies
- Brønsted–Lowry acid–base chemistry
- Buffer solution
- Chemical activity
- Chemical concentration
- Chemical interface
- Colligative property
- Colloid
- Electrolyte solution
- Electrolytic dissociation
- Henry’s law
- Ideal solution
- Ionic strength
- Langmuir adsorption model
- Langmuir’s adsorption and monolayer experiments
- Lewis acid–base chemistry
- Micelle
- Osmosis
- Osmotic pressure
- Raoult’s law
- Solubility equilibrium
- Solute
- Solution
- Solvent
- Surface chemistry
- Surface tension
- Surfactant
- van ’t Hoff osmotic-pressure comparisons
Chemical kinetics & dynamics20
- Activation energy
- Arrhenius equation
- Arrhenius temperature–rate comparisons
- Catalysis
- Chemical kinetics
- Chemical reaction
- Collision theory
- Elementary reaction
- Heterogeneous catalysis
- Homogeneous catalysis
- Photochemistry
- Rate law
- Rate-determining step
- Reaction coordinate
- Reaction mechanism
- Reaction rate
- Steady-state approximation
- Transition state
- Transition-state theory
- Zewail’s femtochemistry experiments
Inorganic & coordination chemistry17
- Bioinorganic chemistry
- Chelation
- Coordination complex
- Coordination number
- Coordination theory
- Crystal-field theory
- Inorganic compound
- Ionic compound
- Ligand
- Ligand substitution
- Ligand-field theory
- Metal–ligand bonding
- Organometallic compound
- Oxidative addition
- Reductive elimination
- Transition-metal chemistry
- Werner’s coordination-isomer studies
Organic chemistry22
- Addition reaction
- Aromaticity
- Carbonyl compound
- Carbonyl group
- Constitutional isomer
- Electrophile
- Elimination reaction
- Enantiomer
- Functional group
- Heterocycle
- Hydrocarbon
- Molecular chirality
- Nucleophile
- Organic compound
- Organic synthesis
- Pasteur’s tartrate resolution
- Pericyclic reaction
- Reaction intermediate
- Retrosynthetic analysis
- Stereochemistry
- Substitution reaction
- Wöhler’s urea synthesis
Analytical chemistry22
- Analytical chemistry
- Bragg X-ray diffraction experiments
- Calibration curve
- Chemical measurement
- Chemical measurement uncertainty
- Chemical reference material
- Chemical sampling
- Chromatography
- Detection limit
- Gas chromatography
- Liquid chromatography
- Mass spectrometry
- Mass-spectrometric isotope-ratio measurement
- Metrological traceability in chemistry
- Qualitative chemical analysis
- Quantitative chemical analysis
- Separation science
- Spectrophotometry
- Standard-addition method
- Titration
- Tsvet’s pigment chromatography experiments
- X-ray crystallography
Electrochemistry23
- Battery
- Butler–Volmer equation
- Cyclic voltammetry
- Electrochemical cell
- Electrochemical corrosion
- Electrochemical double layer
- Electrochemistry
- Electrode
- Electrode kinetics
- Electrode overpotential
- Electrode potential
- Electrolysis
- Electrolyte
- Electrolytic cell
- Faraday’s electrolysis experiments
- Faraday’s laws of electrolysis
- Fuel cell
- Galvanic cell
- Nernst concentration-cell measurements
- Nernst equation
- Redox reaction
- Standard electrode potential
- Voltaic-pile experiments
Radiochemistry15
- Actinide separation chemistry
- Curie radium-separation measurements
- Isotope tracer
- Isotope-dilution analysis
- Libby’s radiocarbon validation measurements
- Neutron-activation analysis
- Nuclear-fuel-cycle chemistry
- Radiation chemistry
- Radioactive decay chain
- Radiocarbon dating
- Radiochemistry
- Radiometric dating
- Radionuclide
- Radiopharmaceutical
- Soddy’s isotope and displacement evidence
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