Perspectives of Light-Front Quantized Field Theory: Some New Results

TL;DR

This paper reviews light-front quantization of relativistic field theory, demonstrating its equivalence to conventional methods and highlighting its advantages in clarity, economy, and causal propagators, with new insights into spontaneous symmetry breaking and QCD.

Contribution

It provides new results confirming the equivalence of light-front and conventional quantization, and discusses its advantages in studying symmetry breaking, vacua, and QCD in a more transparent framework.

Findings

LF quantization is as appropriate as conventional quantization.

LF propagators are causal, enabling Wick rotation and Euclidean analysis.

LF approach offers a more economical and transparent perspective.

Abstract

Some basic topics in the light-front (LF) quantization of relativistic field theory are reviewed. It is argued that the LF quantization is equally appropriate as the conventional one and that they lead, assuming the micro- causality principle, to the same physical content. This is confirmed in the studies on the LF of the spontaneous symmetry breaking (SSB), of the degenerate vacua in Schwinger model (SM) and Chiral SM (CSM), of the chiral boson theory, and of the QCD in covariant gauges among others. The discussion on the LF is more economical and more transparent. In the context of the Dyson-Wick pertur- bation theory the relevant popagators in the front form theory are causal. The Wick rotation can then be performed to employ the Euclidean space integrals in momentum space. The lack of manifest covariance becomes tractable, and still more so if we employ, as discussed in the text, the Fourier transform of the fermionic field based on a special construction of the LF spinor. The fact that the hyperplanes $x^{pm}=0$ constitute characteristic surfaces of the hyper- bolic partial differential equation is found irrelevant in the quantized theory.