Related papers: Coherent states for a quantum particle on a circle
Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
An algebraic formalism for description of quantum states of charged particle with spin moving in two-dimensional space under influence of singular magnetic field is developed in terms of graded algebras. The fundamental assumption is that…
These notes give a mathematical introduction to two seemingly unrelated topics: (i) quantum spin systems and their cycle and loop representations, due to T\'oth and Aizenman-Nachtergaele; (ii) coagulation-fragmentation stochastic processes.…
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…
Unique set of coherent states for the anharmonic oscillator is obtained by requiring i. under the quantum mechanical time evolution a coherent state evolves into another, governed by trajectory in the classical phase space (of a related…
As a toy model for the microscopic description of matter in de Sitter space, we consider a Hamiltonian acting on the spin-j representation of SU(2). This is a model with a finite-dimensional Hilbert space, from which quasinormal modes…
A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After…
The representation theory of the group U(1,q) is discussed in detail because of its possible application in a quaternion version of the Salam-Weinberg theory. As a consequence, from purely group theoretical arguments we demonstrate that the…
We propose an approach to the study of open quantum systems based on a parametric representation of the principal system. The representation is obtained introducing generalized coherent states for the environment, and is such that the…
In this paper, we study the role of coherent states in the realm of quantum cosmology, both in a second-quantized single universe and in a third-quantized quantum multiverse. In particular, most emphasis will be paid to the quantum…
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…
The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its…
This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of $p$-mechanics which is a consistent physical theory capable of…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
We construct a system of coherent states for the hydrogen atom that is expressed in terms of elementary functions. Unlike to the previous attempts in this direction, this system possesses the properties equivalent to the most of those for…
The first two parts of this article surveys results related to the heat-kernel coherent states for a compact Lie group K. I begin by reviewing the definition of the coherent states, their resolution of the identity, and the associated…
We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…
The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an…
We discuss a general model for effective quantum field theories (QFTs), which for example comprises quantum chromodynamics and quantum electrodynamics. We assume in the model a perturbative expansion of the Lagrangian with respect to a…