Poincare invariance in temporal gauge canonical quantization and \(\theta\)-vacua

TL;DR

This paper demonstrates Poincare invariance in the temporal gauge quantization of QCD and explores how different heta-parameters affect the representations of the Poincare group, highlighting the physical irrelevance of heta under certain conditions.

Contribution

It provides a manifest proof of Poincare invariance in temporal gauge QCD and analyzes the impact of heta-terms on Poincare group representations.

Findings

Poincare invariance verified in physical Hilbert space

Different heta-values lead to distinct Poincare representations

heta-parameter is physically irrelevant without further Hilbert space restrictions

Abstract

The Poincare invariance in the temporal gauge canonical quantization of QCD is shown manifestly by verifying the energy-momentum-vector and angular-momentum-tensor satisfy the Poincare algebra in the physical Hilbert space. Two different values of \(\theta\) for the $\theta$-term in QCD lagrangian lead to different representations of the Poincare group, which are, however, connected by an unitary transformation. Thus the parameter \(\theta\) becomes physically irrelevant unless we can further restrict the physical Hilbert space.