Gauge Identities and the Dirac Conjecture

Abstract

The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first class constraints. In the latter approach such local symmetries are reflected in the existence of so called gauge identities. The connection between the two becomes apparent, if one works with a first order Lagrangean formulation. Our analysis applies to purely first class systems. We show that Dirac's conjecture applies to first class constraints which are generated in a particular iterative way, regardless of the possible existence of bifurcations or multiple zeroes of these constraints. We illustrate these statements in terms of several examples.

21 pages

References in corpus (7)

• Antibracket, Antifields and Gauge-Theory Quantization
• Hamiltonian Approach to Lagrangian Gauge Symmetries
• Dynamical Structure of Irregular Constrained Systems
• Recursive Construction of Generator for Lagrangian Gauge Symmetries
• Classification of constraints using chain by chain method
• Lagrange versus Symplectic Algorithm for Constrained Systems
• Lagrangean Approach to Hamiltonian Gauge Symmetries and the Dirac Conjecture

Cited by in corpus (3)

• A First Class Constraint Generates Not a Gauge Transformation, But a Bad Physical Change: The Case of Electromagnetism
• Singular Lagrangians, Constrained Hamiltonian Systems and Gauge Invariance: An Example of the Dirac-Bergmann Algorithm
• Singular Lagrangians and the Dirac--Bergmann Algorithm in Classical Mechanics