Dynamical Structure of the Fields in the Light Cone Coordinates

TL;DR

This paper investigates how the dynamical structure and the number of physical modes in field theories change when using light cone coordinates, revealing a reduction in Schrödinger modes across scalar, spinor, and vector fields.

Contribution

It provides a detailed analysis of the reduction of Schrödinger modes in light cone coordinates and its impact on the dynamical structure of various field theories.

Findings

Number of Schrödinger modes is halved in light cone coordinates

Reduction affects the ladder operators and physical state structure

Differences observed in scalar, spinor, and vector field theories

Abstract

It is well-known that additional constraints emerge in light cone coordinates. We enumerate the number of physical modes in light cone coordinates and compare it with conventional coordinates. We show that the number of Schrodinger modes is divided by two in light cone coordinates. We study the effect of this reduction in the number ladder operators acting on physical states of a system. We analyse the scaler, spinor and vector field theories carefully to see the effect of changes in the dynamical structure of these theories from the view point of the reduction of Schrodinger modes in light-cone coordinates.