Dirac's Observables for the Higgs Model: I) the Abelian Case

Details Dirac's Observables for the Higgs Model: I) the Abelian Case Dirac's Observables for the Higgs Model: I) the Abelian Case

1996-06-13

arxiv.org/abs/hep-th/9606078v1

Int.J.Mod.Phys. A12 (1997) 4769-4796

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, RevTeX

Scientific paper

10.1142/S0217751X97002541

We search a canonical basis of Dirac's observables for the classical Abelian Higgs model with fermions in the case of a trivial U(1) principal bundle. The study of the Gauss law first class constraint shows that the model has two disjoint sectors of solutions associated with two physically different phases. In the electromagnetic phase, the electromagnetic field remains massless: after the determination of the Dirac's observables we get that both the reduced physical Hamiltonian and Lagrangian are nonlocal. In the Higgs phase, the electromagnetic field becomes massive and in terms of Dirac's observables we get a local, but nonanalytic in the electric charge (or equivalently in the sum of the electromagnetic mass and of the residual Higgs field), physical Hamiltonian; however the associated Lagrangian is nonlocal. Some comments on the R-gauge-fixing, the possible elimination of the residual Higgs field and on the Nielsen-Olesen vortex solution close the paper.

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