Selected Topics in Light Front Field Theory and Applications to the High Energy Phenomena

TL;DR

This thesis explores light-front field theory's application to high-energy phenomena, especially deep inelastic scattering, developing a Hamiltonian approach that addresses structure functions directly and confirms its consistency with traditional methods.

Contribution

It introduces a light-front QCD Hamiltonian framework for DIS structure functions, incorporating non-perturbative effects and defining new structure functions using LF gauge and perturbation theory.

Findings

LFQCD approach reproduces known structure functions

New factorization scheme for non-perturbative content

Consistent calculation of anomalous dimensions

Abstract

In this thesis, we have presented some of the aspects of light-front (LF) field theory through their successful application in the Deep Inelastic Scattering (DIS). We have developed a LFQCD Hamiltonian description of the DIS structure functions starting from Bjorken-Johnson-Low limit of virtual forward Compton scattering amplitude and using LF current commutators. We worked in the LF gauge $A^+=0$ and used the old-fashioned LFQCD perturbation theory in our calculations. The importance of our work are summarized below. Our approach shares the intution of parton model and addresses directly the structure functions, which are experimental objects, instead of its moments as in OPE method. Moreover, it can potentially incorporate the non-perturbative contents of the structure functions as we have demonstrated by introducing a new factorization scheme. In the context of nucleonic helicity structure, the well known gauge fixed LF helicity operator is shown to provide consistent physical information and helps us defining new relevant structure functions. The anomalous dimensions relevant for the $Q^2$-evolution of such structure functions are calculated. Our study is important in establishing the equivalance of LF field theory and the usual equal-time one through perturbative calculations of the dressed parton structure functions reproducing the well known results. Also the importance of Gallilean boost symmetry in understanding the correctness of any higher order calculation using ($x^+$)-ordered LFQCD perturbation theory are emphasized.