Time quantization and q-deformations

  title={Time quantization and q-deformations},
  author={Claudio Albanese and Stephan Lawi},
  journal={Journal of Physics A},
We extend to quantum mechanics the technique of stochastic subordination, by means of which one can express any semi-martingale as a time-changed Brownian motion. As examples, we considered two versions of the q-deformed harmonic oscillator in both ordinary and imaginary time and show how these various cases can be understood as different patterns of time quantization rules. 

Figures from this paper

Poisson Bracket in Non-commutative Algebra of Quantum Mechanics
The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying
Chronons, Time Atoms, and Quantized Time: Time Asymmetry Re-Visited
A directional time does not feature in Newtonian mechanics, in electromagnetic theory, in quantum mechanics, in the equations which describe the world of elementary particles (with the exception of
An alternative wavefunction to the description of the dynamic localization of a charged particle moving on a one-dimensional lattice under the influence of a periodic time dependent electric field is
A Modular Operator Approach to Entanglement of Causally Closed Regions
Quantum entanglement is shown for causally separated regions within a conformal quantum mechanical correspondence with conformal radial Killing fields of causal diamonds in Minkowski space. In
Bochner Subordination, Logarithmic Diffusion Equations, and Blind Deconvolution of Hubble Space Telescope Imagery and Other Scientific Data
A powerful blind deconvolution procedure based on postulating system optical transfer functions (otfs) in the form of generalized Linnik characteristic functions is developed, resolving the unexplained appearance of exceptionally low Levy stable exponents in previous work on the same class of images.
The Universe is Like a Hollowed Sphere. The Wave Concept of Time
There is space for new ideas of the essence and the entity of time. The article refers to our time concept as a special wave type and presents results of our investigations on this subject. Thus,


A simple difference realization of the Heisenberg q-algebra
A realization of the Heisenberg q‐algebra whose generators are first‐order difference operators on the full real line is discussed herein. The eigenfunctions of the corresponding q‐oscillator
Quantum and classical mechanics of Q deformed systems
Quantum and classical mechanics of a system of q-deformed bosonic oscillators are considered. The q-deformed Heisenberg-Weyl algebra of creation and destruction operators is realized by differential
On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q
The quantum group SU(2)q is discussed by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum. Such theory of the q-analogue of the quantum harmonic
The quantum group SUq(2) and a q-analogue of the boson operators
A new realisation of the quantum group SUq(2) is constructed by means of a q-analogue to the Jordan-Schwinger mapping, determining thereby both the complete representation structure and q-analogues
Introduction of a quantum of time (chronon), and its consequences for quantum mechanics
In this review-article, we discuss the consequences of the introduction of a quantum of time tau_0 in the formalism of non-relativistic quantum mechanics (QM) by referring ourselves in particular to
On spectral properties ofq-oscillator operators
AbstractThe property of self-adjointness of the operatorQ =a+ +a- in three types ofq-oscillator algebras is considered. Spectral measures and generalized eigenfunctions ofQ are found in the cases
Hilbert spaces of analytic functions and generalized coherent states
Generalized coherent states which are associated with a generalization of the harmonic oscillator commutation relation are investigated. It is shown that these states form an overcomplete basis in a
WKB equivalent potentials for the q-deformed harmonic oscillator
WKB equivalent potentials (WKB-EP) giving the same spectrum as the q-deformed harmonic oscillator with the symmetry SUq(2) are determined. While in the case of q being real the WKB-EP goes to