Relativistic path integral and relativistic Hamiltonians in QCD and QED

TL;DR

This paper derives a new explicit form of the quark-antiquark Green's function using the proper-time path integral, leading to an instantaneous Hamiltonian applicable to mesons in magnetic fields, advancing theoretical understanding in QCD and QED.

Contribution

It introduces a novel parametric form of the Green's function and Hamiltonian for quark-antiquark systems in gluonic and electromagnetic fields.

Findings

Explicit form of the Green's function derived

Hamiltonian solutions provided for mesons in magnetic fields

Enhanced theoretical framework for QCD and QED interactions

Abstract

The proper-time 4d path integral is used as a starting point to derive the new explicit parametric form of the quark-antiquark Green's function in gluonic and QED fields, entering as a common Wilson loop. The subsequent vacuum averaging of the latter allows to derive the instantaneous Hamiltonian. The explicit form and solutions are given in the case of the $q\bar q$ mesons in magnetic field.