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The semidirect product of spacetime translations with the Lorentz group.
The connected, universal-cover, and full disconnected versions must be distinguished in representation theory.
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This is an authored directed relation from the source endpoint to the target endpoint.
For a fixed Minkowski vector space, the Poincaré group is the semidirect product of spacetime translations with the Lorentz group.
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.
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This is an authored directed relation from the source endpoint to the target endpoint.
Poincaré symmetry is mathematically represented by the Poincaré group.
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-poincare_groupnlab-physics-poincare_symmetrynlab-poincare_groupThis 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.
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