相关论文: GROUP QUANTIZATION ON CONFIGURATION SPACE
We analyze the quantization of dynamical systems that do not involve any background notion of space and time. We give a set of conditions for the introduction of an intrinsic time in quantum mechanics. We show that these conditions are a…
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…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
Free-field formalism for quantum groups provides a special choice of coordinates on a quantum group. In these coordinates the construction of associated integrable system is especially simple. This choice also fits into general framework of…
The Group Quantization formalism is a scheme for constructing a functional space that is an irreducible infinite dimensional representation of the Lie algebra belonging to a dynamical symmetry group. We apply this formalism to the…
In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…
We review several procedures of quantization formulated in the framework of (classical) phase space M. These quantization methods consider Quantum Mechanics as a "deformation" of Classical Mechanics by means of the "transformation" of the…
The review is devoted to topological global aspects of quantal description. The treatment concentrates on quantizations of kinematical observables --- generalized positions and momenta. A broad class of quantum kinematics is rigorously…
The purpose of this review is to provide a brief overview of some recent conceptual developments about possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems.…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
The purpose of this paper is twofold: On the one hand, after a thorough review of the matter free case, we supplement the derivations in our companion paper on 'loop quantum gravity without the Hamiltonian constraint' with calculational…
Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Z_n of arbitrary order n=2,3,..., but a larger group - the non-Abelian…
A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides…
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),…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such quantum reference frames need to be modified to take into account the quantum and dynamical features of the reference…
Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…
As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
We formulate the notion of quantum group symmetry of the Hamiltonian corresponding to Potts model and compute it for few simple models. Our examples illustrate how a slight change of the model parameter may result in a drastic change of the…