Related papers: Free particle on SU(2) group manifold
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…
These lectures provide an overview of Quantum Chromodynamics (QCD), the SU(3) gauge theory of the strong interactions. The running of the strong coupling and the associated property of Asymptotic Freedom are analyzed. Some selected…
In this short note, quantum subgroups in finite free products of the Pontryagin duals of free unitary quantum groups are classified. They correspond to pairs of a subgroup $\Gamma$ and a subset $S$ of the free group $\mathbb{F}_n$ such that…
We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and…
The method of geometrical quantization of symplectic manifolds is applied to constructing infinite dimensional irreducible unitary representations of the algebra of functions on the compact quantum group $SU_q(2)$. A formulation of the…
Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.
Based on a geometric picture, the example of free particle motion for both classical and quantum domains is considered in the tomographic probability representation. Wave functions and density operators as well as optical and symplectic…
The new ansatz which is the SO(3) group soliton was defined for the SU(3) Skyrme model. The model is considered in noncanonical bases $SU(3)\supset SO(3)$ for the state vectors. A complete canonical quantization of the model have been…
We present D=3 and D=4 models for massive particles moving in a new type of enlarged spacetime, with D-1 additional vector coordinates, which after quantization lead to the towers of massive higher spin (HS) free fields. Two classically…
Free coherent states for a system with two degrees of freedom is defined. An isomorphism of the space of distributions on 2-adic disc and the space of free coherent states is constructed.
We show an integrality of the quantum SU(2)-invariant associated with a non-trivial first cohomology class modulo two.
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
Let p be an odd prime and r be relatively prime to p. Let G be a finite p-group. Suppose an oriented 3-manifold M-tilde has a free G-action with orbit space M. We consider certain Witten-Reshetikhin-Turaev SU(2) invariants w_r(M). We will…
In this paper, a way is given to obtain explicitly the representations of the Poincar\'e group as can be prescribed by Geometric Quantization. Thus one obtains some forms of the Space of Quantum States of the different relativistic free…
Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups.…
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…
In this note we relate the geometric notion of fill radius with the fundamental group of the manifold. We prove: ''Suppose that a closed Riemannian manifold M satisfies the property that its universal cover has bounded fill radius. Then the…
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…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…
Using the approach alternative to the traditional Thermodynamic Bethe Ansatz, we derive analytical expressions for the free energy of Coqblin-Schrieffer model with arbitrary magnetic and crystal fields. In Appendix we discuss two concrete…