相关论文: Symplectic Cuts and Projection Quantization
A long-standing problem in quantum gravity and cosmology is the quantization of systems in which time evolution is generated by a constraint that must vanish on solutions. Here, an algebraic formulation of this problem is presented,…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
We define spin-c prequantization of a symplectic manifold to be a spin-c structure and a connection which are compatible with the symplectic form. We describe the cutting of an S^1-equivariant spin-c prequantization. The cutting process…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
The aim of this article is to study the functorial properties of the ``formal geometric quantization'' procedure which is defined for non-compact Hamiltonian manifolds (when the moment map is proper). For this purpose, we introduce a…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
We prove several versions of "quantization commutes with reduction" for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin^c structure. Our theorems work whenever the…
By using a generalization of the optical tomography technique we describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a Hamiltonian dynamics in an intrinsic time $\tau$ which samples a…
In a recent paper by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects in…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
We use the ideas of symplectic quantization for quantizing fields in finite volumes. We consider, as examples, the Klein-Gordon and electromagnetic fields in three dif- ferent boxes. As a second idea we consider the given boundary…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a generalized Hamiltonian dynamics in an extra time variable $\tau$ which, at…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Tomograms introduced for the description of quantum states in terms of probability distributions are shown to be related to a standard star-product quantization with appropriate kernels. Examples of symplectic tomograms and spin tomograms…
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…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space-time by means of a generalized microcanonical ensemble similar to the one of the standard…
Systems with constraints pose problems when they are quantized. Moreover, the Dirac procedure of quantization prior to reduction is preferred. The projection operator method of quantization, which can be most conveniently described by…
We propose in this paper an alternative method for the quantisation of systems with first-class constraints. This method is a combination of the coherent-state-path-integral quantisation developed by Klauder, with the ideas of reduced state…