Equivalence of pion loops in equal-time and light-front dynamics

TL;DR

This paper proves that the light-front and equal-time approaches to calculating pion loop corrections in nucleon properties are equivalent, demonstrating this through self-energy calculations with different pion-nucleon couplings.

Contribution

It establishes the equivalence of light-front and equal-time formulations for pionic corrections, including nonanalytic behavior, in a covariant framework.

Findings

Equivalence shown in rest and infinite momentum frames

Derived nonanalytic behavior of nucleon self-energy

Validated equivalence in covariant formulation

Abstract

We demonstrate the equivalence of the light-front and equal-time formulations of pionic corrections to nucleon properties. As a specific example, we consider the self-energy of a nucleon dressed by pion loops, for both pseudovector and pseudoscalar pion-nucleon couplings. We derive the leading and next-to-leading nonanalytic behavior of the self-energy on the light-front, and show explicitly their equivalence in the rest frame and infinite momentum frame in equal-time quantization, as well as in a manifestly covariant formulation.