Field theory of spontaneous symmetry breaking: spontaneous symmetry breaking in scalar quantum electrodynamics
We study spontaneous breakdown of symmetry in scalar quantum electrodynamics. We investigate the effect of spontaneous breakdown of U(1) symmetry on the spectrum and dynamics of particle states in the Abelian Higgs-Guralnik-Kibble model, in which the electromagnetic field is quantized in the Lorentz gauge. We identify a lowest order part of the Hamiltonian that includes the bilinear self mass interactions that are introduced by the spontaneous breakdown of the U(1) symmetry. We show that the spectrum of particle states that is described by this lowest order part of the Hamiltonian includes a vector triad of massive particle states, scalar Higgs particles and massless electrodynamic ghosts. We show that the spontaneous breakdown of the U(1) symmetry does not affect the gauge fixing field. This allows the Gupta-Bleuler subsidiary condition to be imposed as a Lorentz invariant and time independent constraint on the physical state space in a manner similar to that of conventional electrodynamics. We show that it is essential to implement the subsidiary condition properly in this case and it is the coupling of charge to photons in the subsidiary condition that is responsible for endowing the zero helicity mode of a massive vector field with mass. We calculate the effect of an infinitesimal Lorentz boost on the massive transferse photon states and identify a zero helicity mode of a vector triad of helicity states and thereby explicitly demonstrate the operation of the Higgs mechanism. We show that the massive vector boson field is a conventional Proca field. We construct an interaction picture representation and a manifestly covariant S-matrix. We use S-matrix theory to demonstrate the detachment of pure gauge states in the physical subspace and to study renormalization.
- Research Organization:
- Connecticut Univ., Storrs (USA)
- OSTI ID:
- 6298711
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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