Discrete symmetries and the propagator approach to coupled fermions in Quantum Field Theory. Generalities: The case of a single fermion-antifermion pair |
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Authors: | Q Duret |
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Institution: | LPTHE tour 13-14, 4ème étage, UPMC Univ Paris 06, BP 126, 4 place Jussieu, F-75252 Paris Cedex 05, France Unité Mixte de Recherche UMR 7589, CNRS/UPMC Univ Paris 06, France |
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Abstract: | Starting from Wigner’s symmetry representation theorem, we give a general account of discrete symmetries (parity P, charge conjugation C, time-reversal T), focusing on fermions in Quantum Field Theory. We provide the rules of transformation of Weyl spinors, both at the classical level (grassmanian wave functions) and quantum level (operators). Making use of Wightman’s definition of invariance, we outline ambiguities linked to the notion of classical fermionic Lagrangian. We then present the general constraints cast by these transformations and their products on the propagator of the simplest among coupled fermionic system, the one made with one fermion and its antifermion. Last, we put in correspondence the propagation of C eigenstates (Majorana fermions) and the criteria cast on their propagator by C and CP invariance. |
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Keywords: | Spinors Lorentz invariance Discrete symmetries Propagator |
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