Spontaneous symmetry breaking of (1+1)-dimensional $\bf \phi^4$ theory in light-front field theory (III)

TL;DR

This paper studies (1+1)-dimensional $f ^4$ theory using light-front quantization, analyzing zero-mode contributions, renormalization, and critical behavior, confirming known results and exploring nonperturbative aspects.

Contribution

It provides a detailed analysis of zero-mode effects and critical phenomena in light-front $^4$ theory, including nonperturbative solutions and divergence handling.

Findings

Zero-mode contributions match equal-time formulation results.

Critical coupling diverges logarithmically in the broken phase.

Critical exponent agrees with mean field theory.

Abstract

We investigate (1+1)-dimensional $\phi^4$ field theory in the symmetric and broken phases using discrete light-front quantization. We calculate the perturbative solution of the zero-mode constraint equation for both the symmetric and broken phases and show that standard renormalization of the theory yields finite results. We study the perturbative zero-mode contribution to two diagrams and show that the light-front formulation gives the same result as the equal-time formulation. In the broken phase of the theory, we obtain the nonperturbative solutions of the constraint equation and confirm our previous speculation that the critical coupling is logarithmically divergent. We discuss the renormalization of this divergence but are not able to find a satisfactory nonperturbative technique. Finally we investigate properties that are insensitive to this divergence, calculate the critical exponent of the theory, and find agreement with mean field theory as expected.