相关论文: The energy operator for infinite statistics
We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our…
The aim of Part II of this paper is to try to describe wave functions on q-deformed versions of position and momentum space. This task is done within the framework developed in Part I of the paper. In order to make Part II self-contained…
We derive Heisenberg equations for arbitrary high order moments of creation and annihilation operators in the case of the quantum master equation with a multimode generator which is quadratic in creation and annihilation operators and…
The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of "physical experiment" and from five simple Postulates concerning "experimental…
This work gives value to the importance of Hilbert-Schmidt operators in the formulation of a noncommutative quantum theory. A system of charged particle in a constant magnetic field is investigated in this framework.
Crystal tensor operators, which tranform under U_q->0(sl(2)), in analogous way as the vectors of the crystal basis, are introduced. The Wigner-Eckart theorem for the crystal tensor is defined: the selection rules depend on the initial state…
The problem of the `infinite energy' of a point charge is well known in connection with the Lorentz--Abraham--Dirac equation and, more significantly, in quantum electrodynamics. Though it is not stated usually, this is strongly related to…
We consider the energy of the Universe, from the pseudo-tensor point of view(Berman,1981). We find zero values, when the calculations are well-done.The doubts concerning this subject are clarified, with the novel idea that the justification…
The quantum deformation of the oscillator algebra and its implications on the phase operator are studied from a view point of an index theorem by using an explicit matrix representation. For a positive deformation parameter $q$ or…
We construct a new nonlinear deformed Schr\"odinger structure using a nonlinear derivative operator which depends on a parameter $q$. This operator recovers Newton derivative when $q \rightarrow 1$. Using this operator we propose a deformed…
We present in this paper quantum real lines as quantum defomations of the real numbers $\R$.Upon deforming the Heisenberg algebra $\cL$ generated by $(a, a^\dagger)$ in terms of the Moyal $\ast$-product,we first construct q-deformed…
For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as…
In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of St\"ackel equivalent systems for both degenerate and…
The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…
At any resolution level of wavelet expansions the physical observable of the kinetic energy is represented by an infinite matrix which is ``canonically'' chosen as the projection of the operator $-\Delta/2$ onto the subspace of the given…
Physicists showed that the generating function of orbifold elliptic genera of symmetric orbifolds can be written as an infinite product. We show that there exists a geometric factorization on space level behind this infinite product formula…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
We discuss the r\^ole of quantum deformation of Weyl-Heisenberg algebra in dissipative systems and finite temperature systems. We express the time evolution generator of the damped harmonic oscillator and the generator of thermal Bogolubov…
In this paper, we introduce the $q$-Heisenberg algebra in the tensor product space $\otimes^2$. We establish its algebraic properties and provide applications to the theory of non-monogenic functions. Our results extend known constructions…
In the problem of entanglement there exist two different notions. One is the entanglement of a quantum state, characterizing the state structure. The other is entanglement production by quantum operators, describing the action of operators…