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Discrete symmetries as automorphisms of the proper Poincaré group. (English) Zbl 0996.81030
A method to finding discrete transformations in representation spaces of the proper Poincaré group is given. The correspondence between involutory automorphisms of this group and the discrete transformations is established. The scalar field on the proper Poincaré group is introduced and its transformations under outer and inner automorphisms are derived. All the discrete transformations (including space and time reflections, charge conjugation and time reversal) on such a field are obtained. The action of discrete transformations on arbitrary spin-tensor fields is obtained without any use of relativistic wave equations. Extending the proper Poincaré group by discrete transformations, the authors construct explicitly fields carrying corresponding irreducible representations.

##### MSC:
 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
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