Unitarity and Lorentz in variance in QCD for a variety of gauges

TL;DR

This paper extends the Kugo and Ojima formalism for gauge theories, incorporating non-covariant gauges, multiple Hamiltonians, Lorentz invariance, and analyzing Fock space structure, providing a broader understanding of state space in QCD.

Contribution

It generalizes the KO formalism to include non-covariant gauges, multiple Hamiltonians, and Lorentz invariant forms, and analyzes the Fock space structure in gauge theories.

Findings

Allowed states span exactly half of Fock space.

Lorentz invariant forms of KO are not unique.

The formalism accommodates non-covariant gauges.

Abstract

We generalise the Kugo and Ojima formalism henceforth called KO) for the structure of state space in gauge theories, in four respects:- (i) We allow for a more general class of gauge-fixing including non-covariant cases. (ii) We display the two possible Hamiltonians allowed by the KO action. (iii) We give manifestly Lorentz invariant forms of KO, showing that they are not unique. (iv) We analyse the structure of Fock space, proving that the allowed states span exactly half of it (leaving aside pure transverse states).