An Introduction to Light-Front Dynamics for Pedestrians

TL;DR

This paper provides an accessible introduction to light-front dynamics, comparing it with instant form, and explores its applications in free fields, bound states, and power counting, with illustrative examples in lower and higher dimensions.

Contribution

It offers an elementary overview of light-front dynamics, including canonical commutators, Poincare algebra, bound state descriptions, and power counting, with practical examples and comparisons.

Findings

Comparison of canonical commutators in different forms

Illustration of bound states in 1+1D QED

Application of power counting in 3+1D theories

Abstract

In these lectures we hope to provide an elementary introduction to selected topics in light-front dynamics. Starting from the study of free field theories of scalar boson, fermion, and massless vector boson, the canonical field commutators and propagators in the instant and front forms are compared and contrasted. Poincare algebra is described next where the explicit expressions for the Poincare generators of free scalar theory in terms of the field operators and Fock space operators are also given. Next, to illustrate the idea of Fock space description of bound states and to analyze some of the simple relativistic features of bound systems without getting into the wilderness of light-front renormalization, Quantum Electrodynamics in one space - one time dimensions is discussed along with the consideration of anomaly in this model. Lastly, light-front power counting is discussed. One of the consequences of light-front power counting in the simple setting of one space - one time dimensions is illustrated using massive Thirring model. Next, motivation for light-front power counting is discussed and power assignments for dynamical variables in three plus one dimensions are given. Simple examples of tree level Hamiltonians constructed by power counting are provided and finally the idea of reducing the number of free parameters in the theory by appealing to symmetries is illustrated using a tree level example in Yukawa theory.