First class functions in constrained second class systems

2003/10/30 by A. V. Bratchikov, Bratchikov, A. V.
Engineering · Mathematics · Physics and Astronomy · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Geophysics and Sensor Technology #Material Science and Thermodynamics #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0310066

9 pages,misprints corrected

arxiv created 2003/11/06 · arxiv updated 2009/12/01

Abstract

Generators of the algebra of first class functions in a system with second class constraints are found. It is shown that first class functions form algebras with respect to the Dirac bracket and pointwise multiplication.The subspace of functions vanishing on constraint surface are ideals of these algebras. The corresponding quotient algebras are isomorphic to the algebras of phase variables in the Dirac bracket formalism. Explicite expressions for generators and brackets of the algebras under consideration are obtained.

Related

• Realization of the Dirac bracket algebras through first class functions and quantization of constrained systems
• Constrained Dynamical Systems: Separation of Constraints into First and Second Classes
• Quantization of constrained systems as Dirac first class versus second class: a toy model and its implications
• Simplifying the algebra of first class constraints, examples on SO(3) and SO(4)
• Exploring the second class constraint quantization approach proposed by Batalin and Marnelius