Fermions and discrete symmetries in Quantum Field Theory. I. Generalities and the propagator for one flavor.

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 P, C, T and their products, focusing on fermions in Quantum Field Theory. We deal in full generality with unitary and antiunitary operators and put a special emphasis on the linearity and unitarity of charge conjugation. We provide the rules of transformation of Weyl spinors, both at the classical level (grassmanian 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 on the fermionic propagator for one flavor by P, C, T and their products; we show that propagating a Majorana fermion is incompatible with the breaking of both C and CP.

Mots clés: spinors; discrete symmetries; propagator

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

Quentin Duret, Bruno Machet. Fermions and discrete symmetries in Quantum Field Theory. I. Generalities and the propagator for one flavor.. 2008. ⟨hal-00316047v1⟩