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Spontaneous symmetry breaking in light front field theory

L. Martinovic
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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.

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L. Martinovic. 2008-01-28. Spontaneous symmetry breaking in light front field theory. https://doi.org/10.1103/physrevd.78.105009

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