Related papers: Group Approach to the Quantization of the P\"oschl…
We explore the group theoretical underpinning of noncommutative quantum mechanics for a system moving on the two-dimensional plane. We show that the pertinent groups for the system are the two-fold central extension of the Galilei group in…
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
The Galilei group has been taken as the fundamental symmetry for 'nonrelativistic' physics, quantum or classical. Our fully group theoretical formulation approach to the quantum theory asks for some adjustments. We present a sketch of the…
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…
Quantum Hall effect wavefunctions corresponding to the filling factors 1/2p+1, 2/2p+1,..., 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus, the wavefunctions…
Recently, it has been observed that a certain class of classical theories with constraints can be quantized by a mathematical procedure known as Rieffel induction. After a short exposition of this idea, we apply the new quantization theory…
In this paper we develope the main ideas of the quantized version of affinely-rigid (homogeneously deformable) motion. We base our consideration on the usual Schr\"odinger formulation of quantum mechanics in the configuration manifold which…
With the aim to construct a dynamical model with quantum group symmetry, the $q$-deformed Schr\"odinger equation of the harmonic oscillator on the $N$-dimensional quantum Euclidian space is investigated. After reviewing the differential…
We consider a covariant causal set approach to discrete quantum gravity. We first review the microscopic picture of this approach. In this picture a universe grows one element at a time and its geometry is determined by a sequence of…
The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…
In conventional quantum mechanics the quantum particle is a special object, whose properties are described by special concepts and quantum principles. The quantization is a special procedure, which is accompanied by introduction of special…
Is "Gravity" a deformation of "Electromagnetism"? Deformation theory suggests quantizing Special Relativity: formulate Quantum Information Dynamics $SL(2,C)_h$-gauge theory of dynamical lattices, with unifying gauge ``group'' the quantum…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
The quantum group GL_p,q(2) is known to be related to the Jordanian GL_h,h'(2) via a contraction procedure. It can also be realised using the generators of the Hopf algebra G_r,s. We contract the G_r,s quantum group to obtain its Jordanian…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
We examine the unitarity of a class of generalized Maxwell U(1) gauge theories in (2+1) D containing the pseudodifferential operator $\Box^{1-\alpha}$, for $\alpha \in [0,1)$. We show that only Quantum Electrodynamics (QED$_3$) and its…
In this work, we introduce a PT-symmetric infinite-dimensional representation of the Uz(sl(2,R)) Hopf algebra, and we analyse a multiparametric family of Hamiltonians constructed from such representation of the generators of this…
We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the…
The renormalization group (RG) in statistical physics focuses on ground-state properties of equilibrium systems. However, it is unclear how it should be generalized to nonunitary quantum dynamics caused by dissipation and measurement…
A framework to describe a broad class of physical operations (including unitary transformations, dissipation, noise, and measurement) in a quantum optics experiment is given. This framework provides a powerful tool for assessing the…