Dirac's Observables for the SU(3)XSU(2)XU(1) Standard Model

TL;DR

This paper provides a complete Hamiltonian analysis of the Standard Model with Grassmann-valued fermions in the Higgs phase, identifying Dirac observables and deriving a reduced Hamiltonian that reveals nonlocal and local interactions.

Contribution

It offers the first Hamiltonian formulation of the Standard Model in the Higgs phase, explicitly constructing Dirac's observables and analyzing the nonperturbative structure of interactions.

Findings

The reduced Hamiltonian includes nonlocal self-energy parts for electromagnetic and strong interactions.

The weak interactions' self-energy parts are local.

The Fermi 4-fermion interaction reappears nonperturbatively.

Abstract

The complete, missing, Hamiltonian treatment of the standard SU(3)xSU(2)xU(1) model with Grassmann-valued fermion fields in the Higgs phase is given. We bypass the complications of the Hamiltonian theory in the Higgs phase, resulting from the spontaneous symmetry breaking with the Higgs mechanism, by studying the Hamiltonian formulation of the Higgs phase for the gauge equivalent Lagrangian in the unitary gauge. A canonical basis of Dirac's observables is found and the reduced physical Hamiltonian is evaluated. Its self-energy part is nonlocal for the electromagnetic and strong interactions, but local for the weak ones. Therefore, the Fermi 4-fermion interaction reappears at the nonperturbative level.