Spontaneous symmetry breaking of (1+1)-dimensional $ϕ^4$ theory in light-front field theory (II)

Stephan Pinsky; Brett van de Sande

doi:10.1103/physrevd.49.2001

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Spontaneous symmetry breaking of (1+1)-dimensional $ϕ^4$ theory in light-front field theory (II)

Stephan Pinsky·Brett van de Sande

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Abstract

We discuss spontaneous symmetry breaking of (1+1)-dimensional $ϕ^4$ theory in light-front field theory using a Tamm-Dancoff truncation. We show that, even though light-front field theory has a simple vacuum state which is an eigenstate of the full Hamiltonian, the field can develop a nonzero vacuum expectation value. This occurs because the zero mode of the field must satisfy an operator valued constraint equation. In the context of (1+1)-dimensional $ϕ^4$ theory we present solutions to the constraint equation using a Tamm-Dancoff truncation to a finite number of particles and modes. We study the behavior of the zero mode as a function of coupling and Fock space truncation. The zero mode introduces new interactions into the Hamiltonian which breaks the $Z_2$ symmetry of the theory when the coupling is stronger than the critical coupling.

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Stephan Pinsky, Brett van de Sande. 1993-10-22. Spontaneous symmetry breaking of (1+1)-dimensional $ϕ^4$ theory in light-front field theory (II). https://doi.org/10.1103/physrevd.49.2001

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