Light-Front Quantized Field Theory (Spontaneous symmetry breaking. Phase transition in scalar field theory.)

TL;DR

This paper compares light-front and equal-time quantized scalar field theories, analyzing their differences in locality and symmetry breaking, and discusses the nature of phase transitions in the  theory.

Contribution

It demonstrates that light-front quantization can lead to nonlocality and provides a new perspective on spontaneous symmetry breaking and phase transitions in scalar field theory.

Findings

Light-front theory may become nonlocal in the longitudinal coordinate.

Both quantization methods yield the same physical content despite different mechanisms.

The  theory exhibits a second-order phase transition at strong coupling.

Abstract

The field theory quantized on the {\it light-front} is compared with the conventional equal-time quantized theory. The arguments based on the {\it microcausality} principle imply that the light-front field theory may become nonlocal with respect to the longitudinal coordinate even though the corresponding equal-time formulation is local. This is found to be the case for the scalar theory which is quantized by following the Dirac procedure. In spite of the different mechanisms of the spontaneous symmetry breaking in the two forms of dynamics they result in the same physical content. The phase transition in {$(\phi^{4})_{2}$} theory is also discussed. The symmetric vacuum state for vanishingly small couplings is found to turn into an unstable symmetric one when the coupling is increased and may result in a phase transition of the {\it second order} in contrast to the first order transition concluded from the usual variational methods.