Spontaneous symmetry breaking in light front field theory

Abstract

A semiclassical picture of spontaneous symmetry breaking in light front field theory is formulated. It is based on a finite-volume quantization of self-interacting scalar fields obeying antiperiodic boundary conditions. This choice avoids a necessity to solve the zero mode constraint and enables one to define unitary operators which shift scalar field by a constant. The operators simultaneously transform the light-front vacuum to coherent states with lower energy than the Fock vacuum and with non-zero expectation value of the scalar field. The new vacuum states are non-invariant under the discrete or continuous symmetry of the Hamiltonian. Spontaneous symmetry breaking is described in this way in the two-dimensional λϕ^4 theory and in the three-dimensional O(2)-symmetric sigma model. A qualitative treatment of topological kink solutions in the first model and a derivation of the Goldstone theorem in the second one is given. Symmetry breaking in the case of periodic boundary conditions is also briefly discussed.

21 pages, 4 figures, improved content

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Cited by in corpus (8)

• Nonperturbative light-front Hamiltonian methods
• Two-dimensional light-front ${\varphi }^4$ theory in a symmetric polynomial basis
• Application of the light-front coupled-cluster method to ${\varphi }^4$ theory in two dimensions
• Light-front ${\varphi }_{1+1}^4$ theory using a many-boson symmetric-polynomial basis
• Covariant analysis of electromagnetic current on the light cone: exposition with scalar Yukawa theory
• Symmetry breaking in light-front ${\varphi }^4$ theory
• A First Step Towards Effectively Nonperturbative Scattering Amplitudes in the Perturbative Regime
• Scalar theories and symmetry breaking in the light-front coupled-cluster method