On the theory of interacting fields in the Foldy-Wouthuysen representation

Abstract

The overview is devoted to quantum electrodynamics (QED) and the Standard Model in the Foldy-Wouthuysen representation. The Hamiltonian H FW in the form of a power series in charge e is obtained as applied to the electromagnetic interaction in the FW representation. Quantum electrodynamics in lowest-order perturbation theory is examined. Calculations of specific QED processes are presented. For external fermion lines (p f 2 = m 2), a possibility to expand the scattering matrix, in powers of the coupling constant with matrix elements, not including fermion propagators, is shown. To take into account particle-antiparticle interaction, a modification of the Foldy-Wouthuysen representation is proposed. Fermions in the modified FW representation can be in two states that are characterized by the sign of a third component of the isotopic spin T f 3 . The sign of T f 3 is connected with the sign at mass terms in the modified Hamiltonian H FW. Real fermions (p f 2 = m f 2 ), as well as antifermions, can interact with each other, while real fermions with a given sign of T f 3 can only interact with real antifermions with the opposite sign of T f 3 , and vice versa. The formulation of the Standard Model in the FW representation does not necessarily require an interaction of Higgs bosons with fermions. In this approach, the role of Higgs bosons narrows considerably as they are responsible only for gauge invariance of the theory and interact only with gauge bosons. Quantum electrodynamics in the FW representation is invariant under C, P, and T transformations. Weak interaction does not conserve C and P parity, but conserves combined CP parity. The theory allows a connection of CP violation and total or partial violation of isotopic symmetry in the modified Foldy-Wouthuysen representation.