The Poincaré group and its Lorentz subgroup are of great importance because invariance under the Poincaré group is a fundamental symmetry in particle physics. For example, a relativistic quantum field theory must have a Poincaré-invariant Lagrangian. This means that its fields must transform under representations of the Poincaré group and Poincaré invariance must be implemented. Here we will discuss some properties of the Lorentz and Poincaré groups.
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