Natural Hadronic Degrees of Freedom for an Effective QCD Action in the Front Form

Abstract

On the one hand any effective action of the QCD, $S[π,\,ρ,\,ω,\ldots,N,\,\overline N,\,Δ^{3/2},\ldots]$, would involve, at least in principle, a tower of hadronic fields of all spins; on the other hand the front form of the field theory has emerged as an appropriate framework to investigate the high energy behaviour of many systems. Motivated by these simple considerations we present a systematic formalism which explicitly provides the front form fields appropriate for constructing a $S[π,\,ρ,\,ω,\ldots,N,\,\overline N,\,Δ^{3/2},\ldots]$. Further, a transformation matrix $Ω(j)$ is constructed which determines how the front form hadronic fields superimpose to yield the more familiar instant form fields. Explicit results for the front form hadronic fields up to spin two are catalogued in appendixes. For spin one half, the $Ω(1/2)$ coincides with the celebrated ``Melosh transformation.'' The formalism, without explicitly invoking any wave equations, reproduces spin one half front-form results of Lepage and Brodsky, and Dziembowski.