Towards an algorithmisation of the Dirac constraint formalism

TL;DR

This paper develops an algorithmic approach to the Dirac constraint formalism using Groebner basis techniques, enabling systematic computation of constraints and symmetries in polynomial Lagrangian systems.

Contribution

It introduces a novel algorithmic scheme for Dirac constraints, integrating commutative algebra methods with gauge symmetry analysis.

Findings

Successfully applied to light-cone Yang-Mills mechanics with SU(2) gauge group.

Automates the separation of first and second class constraints.

Provides a systematic way to construct local symmetry generators.

Abstract

Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Groebner basis techniques. For a wide class of finite dimensional polynomial degenerate Lagrangian systems, we describe an algorithmic scheme of computation of the complete set of constraints, their separation into subsets of first and second class constraints as well as the construction of a generator of local symmetry transformations. The proposed scheme is exemplified by considering the so-called light-cone Yang-Mills mechanics with an SU(2) gauge structure group.