Related papers: Classical phase space singularities and quantizati…
The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first- and second-class constraints from the point of view of…
Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
A basic problem in quantizing a field in curved space is the decomposition of the classical modes in positive and negative frequency. The decomposition is equivalent to a choice of a complex structure in the space of classical solutions. In…
A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed, and then applied…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
Are the classical singularities of general relativistic spacetimes, normally defined by the incompleteness of classical particle paths, still singular if quantum mechanical particles are used instead? This is the question we will attempt to…
We examine the transition of a particle across the singularity of the compactified Milne (CM) space. Quantization of the phase space of a particle and testing the quantum stability of its dynamics are consistent to one another. One type of…
The process of canonical quantization is redefined so that the classical and quantum theories coexist when \hbar>0, just as they do in the real world. This analysis not only supports conventional procedures, it also reveals new quantization…
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal,…
Canonical quantization has served wonderfully for the quantization of a vast number of classical systems. That includes single classical variables, such as $p$ and $q$, and numerous classical Hamiltonians $H(p,q)$, as well as field…
We discuss to what extent classical singularities persist upon quantization in two simple cosmological models.
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
In this paper we investigate the vanishing of cosmological singularities by quantization. Starting from a 5d Kaluza--Klein approach we quantize, as a first step, the non--spherical metric part and the dilaton field. These fields which are…