arXiv:hep-th/9306017 · International Journal of Modern Physics A

DIRAC VERSUS REDUCED PHASE SPACE QUANTIZATION FOR SYSTEMS ADMITTING NO GAUGE CONDITIONS

MIKHAIL S. PLYUSHCHAY, ALEXANDER V. RAZUMOV

Published Mar 30, 1996• 26 citations

Abstract

The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods for dealing with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of systems under consideration. It is found that the two quantization methods may give similar, or essentially different, physical results, and moreover a class of constrained systems, which can be quantized only by the Dirac method, is discussed. A possible interpretation of the gauge degrees of freedom is given.

DOI: 10.1142/s0217751x96000663

Related papers

Dirac versus reduced phase space quantization for systems admitting no gauge conditions

Plyushchay, M S, Razumov, A V

The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of systems under consideration. It is traced out that the two quantization methods may give similar, or essentially different physical results, and, moreover, a class of constrained systems, which can be quantized only by the Dirac method, is discussed. A possible interpretation of the gauge degrees of freedom is given.

Jan 1, 199620 citations

Dirac versus reduced phase space quantization

Mikhail S. Plyushchay, A. V. Razumov

The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give similar, or essentially different physical results, and, moreover, it is shown that there is a class of constrained systems, which can be quantized only by the Dirac method. A possible interpretation of the gauge degrees of freedom is given. Introduction There are two main methods to quantize the Hamiltonian systems with first class constraints: the Dirac quantization [1] and the reduced phase space quantization [2], whereas two other methods, the path integral method [3, 2] and the BRST quantization [4] being the most popular method for the covariant quantization of gauge-invariant systems, are based on and proceed from them [2, 5]. The basic idea of the Dirac method consists in imposing quantum mechanically the first class constraints as operator conditions on the states for singling out the physical ones [1]. The reduced phase space quantization first identifies the physical degrees of freedom at the classical level by the factorization of the constraint surface with respect to the action of the gauge group, generated by the constraints. Then the resulting Hamiltonian system is quantized as a usual unconstrained system [2]. Naturally, the problem of the relationship of these two methods arises. It was discussed in different contexts in literature [6], and there is an opinion that the differences between the two quantization methods can be traced out to a choice of factor ordering in the construction of various physical operators.

arXiv:hep-th/9412137Cambridge University Press eBooksJan 5, 199511 citations

Dirac versus Reduced Quantization and Operator Ordering

K. Shimizu

We demonstrate an equivalence between Dirac quantization and reduced phase space quantization. The equivalence of the two quantization methods determines the operator ordering of the Hamiltonian. Some examples of the operator ordering are shown in simple models.

arXiv:gr-qc/9601042Progress of Theoretical PhysicsJan 1, 19972 citations

Constrained quantization on symplectic manifolds and quantum distribution functions

George Jorjadze

A quantization scheme based on the extension of phase space with application of constrained quantization technique is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar product on the reduced Hilbert space is investigated and a possible solution to this problem is given. Generalization of the Gupta–Bleuler-like conditions is done by minimization of quadratic fluctuations of quantum constraints. The scheme for the construction of generalized coherent states is considered and relation with Berezin quantization is found. The quantum distribution functions are introduced and their physical interpretation is discussed.

arXiv:hep-th/9606162Journal of Mathematical PhysicsJun 1, 19974 citations

Dirac versus reduced quantization and operator ordering

K Shimizu

We show an equivalence between Dirac quantization and the reduced phase space quantization. The equivalence of the both quantization methods determines the operator ordering of the Hamiltonian. Some examples of the operator ordering are shown in simple models. I.

Jan 1, 19961 citation

Quantization of constrained systems and path integrals in curvilinear supercoordinates

Sergie V. Shabanov

For systems with constraints the issue of non-commutability of quantization and elimination of non-physical variables is studied in the framework of path integrals (PIs). It is shown that one should take into consideration the curvilinearity of physical variables and their phase space reduction in order to provide a one-to-one correspondence between the Dirac scheme and PI description. The latter leads to a modification of the standard PI (PI with a gauge condition). A general PI derivation is suggested for any method of picking out physical variables which corresponds to the Dirac scheme.

Journal of Physics A Mathematical and GeneralMar 21, 19917 citations