An extension of the Dirac theory of constraints

TL;DR

This paper extends Dirac's theory of constraints to handle more complex cases where kernel distributions are nonintegrable or of nonconstant rank, and where constraint sets may not be closed, broadening its applicability.

Contribution

It introduces a generalized framework for Dirac's constraint theory accommodating nonintegrable kernels and non-closed constraint sets, which were not addressed in the original formulation.

Findings

Extended Dirac theory to nonintegrable kernel distributions

Generalized constraints to nonconstant rank cases

Broadened applicability to non-closed constraint sets

Abstract

Constructions introduced by Dirac for singular Lagrangians are extended and reinterpreted to cover cases when kernel distributions are either nonintegrable or of nonconstant rank, and constraint sets need not be closed.