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A group action on a vector space by invertible linear maps.
wp-group-representationnlab-representationetingof-representation-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require the group action maps to be invertible linear transformations.
Feed several structures into a construction junction and impose compatibility between them.
wp-group-representationnlab-representationetingof-representation-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Lattice translations act on one-particle states by commuting unitary operators. A Bloch state transforms in a one-dimensional character of that Abelian translation group, labeled by crystal momentum modulo the reciprocal lattice.
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-group-representationwp-physics-bloch-theoremtong-solid-state-physicsmit-theory-of-solidsThis is an authored directed relation from the source endpoint to the target endpoint.
A finite-dimensional group representation assigns a linear operator to each group element; taking its trace produces the associated character and discards basis-dependent matrix entries.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
etingof-representation-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Clebsch–Gordan coefficients implement the change of basis for decomposing tensor-product representations.
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.
wp-group-representationnlab-representationetingof-representation-theorywp-clebsch_gordan_coefficientnlab-clebsch_gordan_coefficientpdg-2026-mathematical-toolsnist-atomic-spectroscopyThis is an authored directed relation from the source endpoint to the target endpoint.
Relativistic particle species and internal quantum numbers are organized by representations of spacetime and internal symmetry groups.
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.
cern-qft-intropdg-standard-modelwp-physics-elementary_particlepdg-rppwp-group-representationThis is an authored directed relation from the source endpoint to the target endpoint.
Irreducibility excludes proper nonzero invariant subspaces.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-irreducible_representationnlab-irreducible_representationThis is an authored directed relation from the source endpoint to the target endpoint.
A unitary representation acts by unitary operators on a Hilbert space.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-unitary_representationnlab-unitary_representation