Physical unitarity in the Lagrangian Sp(2)-symmetric formalism

TL;DR

This paper investigates the structure of state vector space and formulates unitarity conditions for the S-matrix in gauge theories using the Lagrangian Sp(2)-symmetric quantization framework, supported by simple model examples.

Contribution

It develops a detailed analysis of state space structure and unitarity conditions within the Lagrangian Sp(2)-symmetric formalism for gauge theories, providing new theoretical insights.

Findings

Formulated physical S-matrix unitarity conditions.

Analyzed state vector space structure in Sp(2)-symmetric gauge theories.

Illustrated results with simple gauge theory models.

Abstract

The structure of state vector space for a general (non-anomalous) gauge theory is studied within the Lagrangian version of the $Sp(2)$-symmetric quantization method. The physical {\it S}-matrix unitarity conditions are formulated. The general results are illustrated on the basis of simple gauge theory models.