Related papers: Gamow Functionals on Operator Algebras

After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's bra-ket…

The aim of this note is to present a self-contained proof of the fact that a function can be approximated using a linear combination of Gaussian coherent states, with a number of terms controlled in terms of the smoothness and of the decay…

A set of gauge transformations of a relativistic field of quantum harmonic oscillators is studied in a mathematically rigorous manner. Each wave function in the domain of the number operator of a single oscillator generates a…

We introduce a class of monotone $\sigma$-complete effect algebras, called representable, which are $\sigma$-homomorphic images of a class of monotone $\sigma$-complete effect algebras of functions taking values in the interval $[0,1]$ and…

We define two recursive functions obtained by decomposition of a given interval into four close parts and prove two lemmas which determine features of these functions.

$\Gamma$-conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points. We classify these algebras and their representations in terms of Lie algebras and their…

Global internal symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to extended observables by considering unitary actions of finite global 2-group symmetries…

We derive integral representations in terms of the Macdonald functions for the square modulus $s\mapsto | \Gamma ( a + i s ) |^2$ of the Gamma function and its Fourier transform when $a<0$ and $a\not= -1,-2,\ldots $, generalizing known…

We consider renewal shot noise processes with response functions which are eventually nondecreasing and regularly varying at infinity. We prove weak convergence of renewal shot noise processes, properly normalized and centered, in the space…

An explicit counterexample shows that contrary to the situation in the special Colombeau algebra, positivity and invertibility cannot be characterized pointwise in algebras of tempered generalized functions. Further a point value…

Given a bounded open set $\Omega\subset \mathbb{R}^n$, we study sequences of quadratic functionals on the Sobolev space $H^1_0(\Omega)$, perturbed by sequences of bounded linear functionals. We prove that their $\Gamma$-limits, in the weak…

Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in…

Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…

The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…

Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are…

We consider the set of power functions defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative…

In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…

A complete description of resonances for rational toral Anosov diffeomorphisms preserving certain Reinhardt domains is presented. As a consequence it is shown that every homotopy class of two-dimensional Anosov diffeomorphisms contains maps…

Euler's Gamma function $\Gamma$ either increases or decreases on intervals between two consequtive critical points. The inverse of $\Gamma$ on intervals of increase is shown to have an extension to a Pick-function and similar results are…

Let $\Gamma$ be an oriented Jordan smooth curve and $\alpha$ be a diffeomorphism of $\Gamma$ onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertiblity of the binomial functional…