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A framework in which fields are quantum degrees of freedom, supporting many-body and variable-particle-number descriptions. Relativistic QFT additionally imposes relativistic symmetry and causal locality and naturally accommodates antiparticles and scattering.
Relativistic QFT underlies the Standard Model; nonrelativistic quantum field theories also provide effective descriptions of many-body and condensed-matter systems.
wp-physics-quantum_field_theorynlab-physics-quantum_field_theorycern-qft-introtong-qftEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Canonical quantization is one route to QFT formulations.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-canonical_quantizationnlab-physics-canonical_quantizationwp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Canonical or path-integral quantization of a classical field theory is a standard route to a QFT, although quantum consistency and renormalization can alter the admissible theory.
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.
cern-qft-introwp-physics-quantum_field_theorynlab-physics-quantum_field_theorywp-physics-classical_field_theorynlab-physics-classical_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Free fields and asymptotic particle states are naturally represented in Fock space. Generic interacting QFT need not admit a global particle interpretation or a Fock representation unitarily equivalent to the free one.
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.
tong-qftwp-fock_spacenlab-fock_spaceThis is an authored directed relation from the source endpoint to the target endpoint.
Local relativistic QFT imposes locality or causal commutativity in an appropriate formulation.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-locality_principlenlab-physics-locality_principlewp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Path-integral quantization is one major QFT formulation.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-path_integral_quantizationnlab-physics-path_integral_quantizationwp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Relativistic QFT in Minkowski spacetime carries a unitary Poincaré action.
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.
wp-physics-quantum_field_theorynlab-physics-quantum_field_theorywp-poincare_groupnlab-poincare_groupThis is an authored directed relation from the source endpoint to the target endpoint.
Local field operators are formal ingredients of common QFT formulations.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
QFT incorporates quantum states, observables, amplitudes, and probabilistic prediction while allowing fields and variable particle number.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-quantum_field_theorynlab-physics-quantum_field_theorywp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Relativistic QFT in Minkowski spacetime incorporates Lorentz/Poincaré symmetry and causal locality; QFT as a general framework can also be formulated on curved or nonrelativistic backgrounds.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
cern-qft-introwp-physics-quantum_field_theorynlab-physics-quantum_field_theorywp-physics-special_relativitynlab-physics-special_relativityEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Relativistic QFT naturally includes antiparticle sectors for charged fields.
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
wp-physics-antiparticlenlab-physics-antiparticlewp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Nonrelativistic quantum-field and many-body operator methods describe variable occupation, collective modes, symmetry breaking, and low-energy excitations in condensed matter. Condensed-matter physics also uses methods not organized as relativistic QFT.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-quantum_field_theorywp-physics-condensed-mattertong-solid-state-physicsmit-theory-of-solidsThis is an authored directed relation from the source endpoint to the target endpoint.
Correlation functions encode QFT observables and dynamics.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-correlation_functionnlab-physics-correlation_functionwp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Local Lorentz-invariant QFT with the usual spectral and unitarity assumptions obeys CPT symmetry.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-physics-quantum_field_theorynlab-physics-quantum_field_theorycern-qft-introtong-qftwp-physics-cpt_theoremnlab-physics-cpt_theorempdg-rppThis is an authored directed relation from the source endpoint to the target endpoint.
Effective field theory is a scale-organized use of QFT with a specified cutoff and degrees of freedom.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-effective_field_theorynlab-physics-effective_field_theorywp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Free QFTs have quadratic actions and no interactions.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-free_quantum_fieldnlab-physics-free_quantum_fieldwp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
The Standard Model interactions are described by relativistic quantum gauge field theories.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
cern-qft-introcern-standard-modelwp-physics-gauge_field_theorynlab-physics-gauge_field_theorywp-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Interacting QFTs include nonquadratic couplings.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-quantum_field_theorynlab-physics-interacting_quantum_fieldnlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Quantize matter fields on the same classical curved spacetime with appropriate state and asymptotic conditions.
Feed several structures into a construction junction and impose compatibility between them.
tong-qfteinstein-online-black-holesThis is an authored directed relation from the source endpoint to the target endpoint.
QFT supports multiparticle states and variable particle number.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-occupation_number_statenlab-fock_spacewp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Nonrelativistic quantum mechanics emerges as a low-energy effective description of suitable QFT sectors when pair creation and relativistic corrections are suppressed.
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.
wp-physics-quantum_mechanicsnlab-physics-quantum_mechanicswp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Stable particles correspond to one-particle asymptotic sectors or representations when they exist.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-one_particle_statenlab-fock_spacewp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Perturbative QFT is a loop or coupling expansion around a solvable theory. It is often asymptotic rather than convergent and is quantitatively useful only in appropriate coupling and kinematic regimes.
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.
wp-physics-quantum_perturbation_theorynlab-physics-perturbative_qftwp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Quantization and regularization can obstruct classical symmetries, producing anomalies.
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
wp-physics-quantum_field_theorynlab-physics-quantum_field_theorycern-qft-introtong-qftwp-physics-quantum_anomalynlab-physics-quantum_anomalybilal-anomaliestong-gaugeThis is an authored directed relation from the source endpoint to the target endpoint.
Perturbative and lattice formulations introduce regulators to define intermediate quantities.
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.
wp-physics-regularizationnlab-physics-regularizationwp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
QFT defines an -matrix when asymptotic particle states and suitable long-time limits exist.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-s_matrixnlab-physics-s_matrixwp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
The spin–statistics connection follows under the stated structural assumptions, not from spin labels alone.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-physics-quantum_field_theorynlab-physics-quantum_field_theorycern-qft-introtong-qftwp-physics-spin_statistics_theoremnlab-physics-spin_statistics_theoremThis is an authored directed relation from the source endpoint to the target endpoint.
QFT can have vacua that do not preserve all symmetries of the action.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-spontaneous_symmetry_breakingnlab-physics-spontaneous_symmetry_breakingwp-physics-quantum_field_theorynlab-physics-quantum_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
A QFT may have one or more vacuum states relative to its dynamics and spacetime.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-vacuum_statenlab-physics-vacuum_statewp-physics-quantum_field_theorynlab-physics-quantum_field_theory