Related papers: Algebraic Constraint Quantization and the Pseudo-R…
This paper explores in some detail a recent proposal (the Rieffel induction/refined algebraic quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this…
This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called ``rigging maps'' associated with Refined Algebraic Quantization, a particular realization of the Dirac…
Starting from the structural similarity between the quantum theory of gauge systems and that of the Kepler problem, an SU(2) gauge description of the five-dimensional Kepler problem is given. This non-abelian gauge system is used as a…
We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a…
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…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
We investigate refined algebraic quantisation with group averaging in a constrained Hamiltonian system whose gauge group is the connected component of the lower triangular subgroup of SL(2,R). The unreduced phase space is T^*R^{p+q} with…
We provide a detailed comparison of the different approaches available for the quantization of a totally constrained system with a constraint algebra generating the non-compact $SL(2,\mathbb{R})$ group. In particular, we consider three…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
We study the deformation quantisation (Moyal quantisation) of general constrained Hamiltonian systems. It is shown how second class constraints can be turned into first class quantum constraints. This is illustrated by the O(N) non-linear…
In a previous work [J. Math. Phys. 52, 123504 (2011)], refined algebraic quantisation (RAQ) within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling one momentum-type constraint…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
The algebra of constraints arising in the canonical quantization of N=1 supergravity in four dimensions is investigated. Using the holomorphic action, the structure functions of the algebra are given and it is shown that the algebra does…
We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in the framework of compact quantum group theory and…
The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a…
We investigate refined algebraic quantisation with group averaging in a finite-dimensional constrained Hamiltonian system that provides a simplified model of general relativity. The classical theory has gauge group SL(2,R) and a…
Refined Algebraic Quantization and Group Averaging are powerful methods for quantizing constrained systems. They give constructive algorithms for generating observables and the physical inner product. This work outlines the current status…
Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
We review the framework of Refined Algebraic Quantization and the method of Group Averaging for quantizing systems with first-class constraints. Aspects and results concerning the generality, limitations, and uniqueness of these methods are…