Unified Constrained Dynamics

TL;DR

This paper introduces a new formulation of unified constrained dynamics that avoids Dirac splitting, providing a closed algebra and a nilpotent operator for constructing the Unitarizing Hamiltonian.

Contribution

It presents a novel approach to unified constrained dynamics without Dirac splitting, including a closed algebra and a nilpotent generating operator.

Findings

Formulation without Dirac splitting

Closed algebra of constraints

Nilpotent generating operator

Abstract

The unified constrained dynamics is formulated without making use of the Dirac splitting of constraint classes. The strengthened, completely--closed, version of the unified constraint algebra generating equations is given. The fundamental phase variable supercommutators are included into the unified algebra as well. The truncated generating operator is defined to be nilpotent in terms of which the Unitarizing Hamiltonian is constructed.