Discrete symmetries and the propagator approach to coupled fermions in Quantum Field Theory. Generalities. The case of a single fermion-antifermion pair.

Quentin Duret (1) , Bruno Machet (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Mots clés: spinors; discrete symmetries; propagator

Domaines: Physique des Hautes Energies - Phénoménologie [hep-ph]; Physique des Hautes Energies - Théorie [hep-th]

Quentin Duret, Bruno Machet. Discrete symmetries and the propagator approach to coupled fermions in Quantum Field Theory. Generalities. The case of a single fermion-antifermion pair.. Annals of Physics, 2010, 325, pp.2041-2074. ⟨10.1016/j.aop.2010.05.016⟩. ⟨hal-00316047v2⟩