Symmetries of Spacetime

The symmetries of spacetime are collectively called the Poincare symmetry. Particles are irreducible representations of the Poincare group which means that they change in ways governed by Poincare symmetry. The subset of Poincare symmetry that is formulated to automatically obey the symmetries of Einstein’s special relativity is called the Lorentz symmetry. It deals only with rotations and change of inertial frames. Quantum fields, which “give rise” to particles, are irreducible representations of the Lorentz group.