Split Involution Coupled to Actual Gauge Symmetry

TL;DR

This paper extends the split involution quantization scheme to systems with both first- and second-class constraints, maintaining Sp(2) symmetry and defining a new equivalence criterion for physical operators and states.

Contribution

It introduces an extended formalism for split involution quantization that incorporates irreducible first-class constraints while preserving symmetry and defining a new physical equivalence criterion.

Findings

Formulation of constraint algebra generating equations

Construction of the Unitarizing Hamiltonian

Definition of physical operators and states with a new equivalence criterion

Abstract

The split involution quantization scheme, proposed previously for pure second--class constraints only, is extended to cover the case of the presence of irreducible first--class constraints. The explicit Sp(2)--symmetry property of the formalism is retained to hold. The constraint algebra generating equations are formulated and the Unitarizing Hamiltonian is constructed. Physical operators and states are defined in the sense of the new equivalence criterion that is a natural counterpart to the Dirac's weak equality concept as applied to the first--class quantities.