Effective Quantum Dynamics of Quarks and Gluons in a Stochastic Background

TL;DR

This paper derives an effective quantum description of quarks and gluons in a stochastic background, revealing that scalars are non-propagating and leading to a confining four-fermion interaction.

Contribution

It provides a detailed derivation of the effective gluon and fermion dynamics in a stochastic gauge background, highlighting the non-propagating nature of scalars and confinement mechanisms.

Findings

Scalar degrees of freedom are non-propagating in the stochastic background.

Stochastic averaging results in a confining four-fermion interaction.

Effective action shows fermions decay exponentially.

Abstract

The quantum dynamics of quarks, gluons and the scalar degrees of freedom associated with the non-linear regime of the non-linear gauge is derived. We discuss the subtleties in quantizing in a stochastic background. Then we show in detail that the stochastic average of the Yang-Mills action is only dependent on the gluon and not on the scalars thus proving that the scalars are non-propagating. Integrating out the scalars from the stochastically averaged fermion action leads to fermions that decline exponentially. Finally, we derive the effective action of the gluons and fermions resulting from stochastic averaging. We show that it leads to a confining four-fermi interaction.