Weak Dirac bracket construction and the superparticle covariant quantization problem

Abstract

The general procedure of constructing a consistent covariant Dirac-type bracket for models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial constraints into infinitely reducible first and second class ones (by making use of some appropriately constructed covariant projectors). Reducibility of the second class constraints involved manifests itself in weakening some properties of the bracket as compared to the standard Dirac one. In particular, a commutation of any quantity with the second class constraints and the Jacobi identity take place on the second class constraints surface only. The developed procedure is realized for N=1 Brink--Schwarz superparticle in arbitrary dimension and for N=1, D=9 massive superparticle with Wess--Zumino term. A possibility to apply the bracket for quantizing the superparticles within the framework of the recent unified algebra approach by Batalin and Tyutin [20--22] is examined. In particular, it is shown that for D=9 massive superparticle it is impossible to construct Dirac-type bracket possessing (strong) Jacobi identity in a full phase space.

21 pages, LaTeX

Cited by in corpus (10)

• Lagrange structure and quantization
• Covariant Quantization of the Brink-Schwarz Superparticle
• Non-Abelian Conversion and Quantization of Non-scalar Second-Class Constraints
• Casimir invariants and the Jacobi identity in Dirac's theory of constrained Hamiltonian systems
• On the Dirac Approach to Constrained Dissipative Dynamics
• Siegel superparticle, higher order fermionic constraints, and path integrals
• Supplementation of reducible constraints and the Green-Schwarz superstring
• The Jacobi identity for Dirac-like brackets
• A modification of the 10d superparticle action inspired by the Gupta-Bleuler quantization scheme method
• Reducible second-class constraints of order L: An irreducible approach