Classical fields on the null-plane

Abstract

The description of the dynamics of the physical systems requires the specification of the evolution of the quantities that determine them in passing from one three-dimensional surface to the other, each one of them defined by the constant value of a parameter called «time». But such surfaces and such time can be chosen in different manners, as it was shown by Dirac in 1949; the inequivalent possible choices are called «dynamical forms». In this study we precisely define them, focusing in particular in the so-called «light-front dynamics» or «null-plane dynamics», in which the time is a coordinate defined on the light-cone. We study the classical free fields in this formulation: the scalar, fermion, electromagnetic and massive vector ones, establishing the solution to their initial-value problem (Goursat’s problem), the classification of their components as dynamical and non-dynamical, and their polarization states. We finalize by highlighting the advantages and disadvantages of null-plane physics, hoping to provide a relevant initiation material to this promising, although generally unknown, area of physics.

Keywords
Classical field theory; light-front dynamics; null-plane dynamics