Related papers: A Uniqueness Theorem for Constraint Quantization
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…
In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
The goal of this paper is to propose and discuss a practical way to implement the Dirac algorithm for constrained field models defined on spatial regions with boundaries. Our method is inspired in the geometric viewpoint developed by Gotay,…
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…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
This is an introduction to the author's recent work on constrained systems. Firstly, a generalization of the Marsden-Weinstein reduction procedure in symplectic geometry is presented - this is a reformulation of ideas of Mikami-Weinstein…
The method of refined algebraic quantization of constrained systems which is based on modification of the inner product of the theory rather than on imposing constraints on the physical states is generalized to the case of constrained…
It is shown that the Dirac approach to Hamiltonization of singular theories can be slightly modified in such a way that primary Dirac constraints do not appear in the process. According to the modified scheme, Hamiltonian formulation of…
The Dirac method of canonical quantization of theories with second class constraints has to be modified if the constraints depend on time explicitly. A solution of the problem was given by Gitman and Tyutin. In the present work we propose…
A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…
The Dirac-Bergmann algorithm for the Hamiltonian analysis of constrained systems is a nice and powerful tool, widely used for quantization and non-perturbative counting of degrees of freedom. However, certain aspects of its application to…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we…
In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…
In this paper we present a theory of reduction of quantum systems in the presence of symmetries and constraints. The language used is that of Lie--Jordan Banach algebras, which are discussed in some detail together with spectrum properties…
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…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
We review the Dirac formalism for dealing with constraints in a canonical Hamiltonian formulation and discuss gauge freedom and display constraints for gauge theories in a general context. We introduce the Dirac bracket and show that it…
We present a novel framework for quantizing constrained quantum systems in which the processes of quantization and constraint enforcement are performed simultaneously. The approach is based on an extension of the stationary action…