Confinement within the use of Minkowski space integral representation

TL;DR

This paper introduces a novel technique to determine spectral functions in Yang-Mills and quenched QED, revealing solutions with branch cuts but no poles, with implications for QCD and Standard Model computations.

Contribution

The paper presents a new method for calculating spectral functions that avoids poles and reveals branch cut structures in gauge theories.

Findings

Spectral functions exhibit branch cuts without poles in the first Riemann sheet.

New solutions found in quenched QED with implications for fermionic spectral analysis.

Method applicable to QCD and Standard Model calculations.

Abstract

We determine the gluonic spectral function $SU(3)$ Yang-Mills theory as well as we found fermionic spectral functions in the strong quenched QED where we found new solutions. Our novel technique provides solutions with the usual branch cut for propagators while not showing any pole structure at the first Riemann sheet (identical with entire complex plane) of complex square of momentum. Implications and further utilizations are briefly adressed for QCD and Standard model calculations.