Related papers: Quantization commutes with reduction in the non-co…
The representations of a group of gauge automorphisms of the canonical commutation or anticommutation relations which appear on the Hilbert spaces of isometries H_\rho implementing quasi-free endomorphisms \rho on Fock space are studied.…
Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are…
Various two-dimensional O(N) models coupled to Euclidean quantum gravity, whose intrinsic dimension is four, are shown to belong to universality classes of nongravitating statistical models in a lower number of dimensions. It is speculated…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
't Hooft has recently developed a discretisation of (2+1) gravity which has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe several models in the continuum…
Quantum transport in a class of nonlinear extensions of the Rudner-Levitov model is numerically studied in this paper. We show that the quantization of the mean displacement, which embodies the quantum coherence and the topological…
The Hamiltonian treatment of constrained systems in $G\ddot{u}ler's$ formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a…
Evidences have suggested that counting representations are sometimes tractable even when the corresponding classification problem is almost impossible, or "wild" in a precise sense. Such counting problems are directly related to matrix…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
We show that non-relativistic and relativistic mechanical systems on a configuration space Q can be seen as the conservative Dirac constraint systems with zero Hamiltonians on different subbundles of the same cotangent bundle T^*Q. The…
In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of…
Geometric quantization transforms a symplectic manifold with Lie group action to a unitary representation. In this article, we extend geometric quantization to the super setting. We consider real forms of contragredient Lie supergroups with…
We canonically quantize multi-component scalar field theories in the presence of solitons. This extends results of Tomboulis to general soliton moduli spaces. We derive the quantum Hamiltonian, discuss reparameterization invariance and…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…
Let $G$ be a real reductive Lie group, $L$ a compact subgroup, and $\pi$ an irreducible admissible representation of $G$. In this article we prove a necessary and sufficient condition for the finiteness of the multiplicities of $L$-types…
Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based…
The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…
This paper studies holomorphic semicocycles over semigroups in the unit disk, which take values in an arbitrary unital Banach algebra. We prove that every such semicocycle is a solution to a corresponding evolution problem. We then…
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in…