Representation theory of the Poincaré group

The representation theory of the Poincaré group is a mathematical framework that studies how the symmetries of spacetime, described by the Poincaré group, act on physical systems, particularly in the context of relativistic quantum mechanics and quantum field theory. ### 1. **Poincaré Group:** The Poincaré group combines both rotations and translations in spacetime, which reflects the symmetries of Minkowski spacetime—a key structure in special relativity.