Gauges, propagators, and physics

TL;DR

This paper discusses a method to derive physical observables in gauge theories like QCD by starting from elementary particles and using a combination of lattice and continuum methods, ensuring gauge invariance in the final results.

Contribution

It outlines a step-by-step approach to connect elementary degrees of freedom to physical states in gauge theories, integrating lattice and functional methods.

Findings

Constructs physical states from elementary constituents.

Uses combined lattice and continuum techniques.

Ensures gauge invariance of final observables.

Abstract

When a theory shall be described at all scales, it is necessary to start from its elementary degrees of freedom. Herein, one possible chain of steps for this purpose will be briefly outlined for the example of a gauge theory, like QCD. Starting with the elementary constituents, gluons and quarks, step by step the final observables, physical states, will be built up. This process is based on the elementary correlation functions, and uses a combination of both numerical lattice calculations and functional continuum methods. While the process uses a fixed gauge at each intermediate step, the final observables are gauge-invariant.