Spontaneous Symmetry Breaking at Infinite Momentum without P+ Zero-Modes

TL;DR

This paper investigates the role of zero-modes in quantum field theory at infinite momentum and demonstrates that spontaneous symmetry breaking can be accurately described without zero-modes in 1+1 dimensions.

Contribution

It shows that zero-modes are not necessary for describing spontaneous symmetry breaking in scalar quantum field theory at infinite momentum.

Findings

Spontaneous symmetry breaking can be modeled without zero-modes.

Zero-modes are not essential for the physics of SSB in 1+1 dimensions.

The nonrelativistic interpretation remains valid without zero-modes.

Abstract

The nonrelativistic interpretation of quantum field theory achieved by quantization in an infinite momentum frame is spoiled by the inclusion of a mode of the field carrying p+=0. We therefore explore the viability of doing without such a mode in the context of spontaneous symmetry breaking (SSB), where its presence would seem to be most needed. We show that the physics of SSB in scalar quantum field theory in 1+1 space-time dimensions is accurately described without a zero-mode.