Body Fixed Frame, Rigid Gauge Rotations and Large N Random Fields in QCD

TL;DR

This paper introduces a novel 'body fixed frame' approach in QCD, analyzing rigid gauge rotations, static and dynamic quarks, and large N random fields, leading to gauge-invariant variational equations and insights into quark interactions.

Contribution

It develops a new framework using the 'body fixed frame' in QCD, studying rigid gauge rotations and large N random fields, with a gauge-invariant variational equation and implications for quark interactions.

Findings

Rigid gauge rotations are studied via Schrödinger equations.

Large N limit treats gauge fields as maximally random under constraints.

Gauge invariance links background fields to quark-quark interactions.

Abstract

The "body fixed frame" with respect to local gauge transformations is introduced. Rigid gauge "rotations" in QCD and their \Sch equation are studied for static and dynamic quarks. Possible choices of the rigid gauge field configuration corresponding to a nonvanishing static colormagnetic field in the "body fixed" frame are discussed. A gauge invariant variational equation is derived in this frame. For large number N of colors the rigid gauge field configuration is regarded as random with maximally random probability distribution under constraints on macroscopic--like quantities. For the uniform magnetic field the joint probability distribution of the field components is determined by maximizing the appropriate entropy under the area law constraint for the Wilson loop. In the quark sector the gauge invariance requires the rigid gauge field configuration to appear not only as a background but also as inducing an instantaneous quark-quark interaction. Both are random in the large N limit.