Related papers: The Gamow Functional
The formalism of quantum systems with diagonal singularities is applied to describe scattering processes. Well defined states are obtained for infinite time, which are related to a ''weak form'' of intrinsic irreversibility. Real and…
Antonymous functions are real-valued functions on the Stone spectrum of a von Neumann algebra R. They correspond to the self-adjoint operators in R, which are interpreted as observables in quantum physics. Antonymous functions turn out to…
The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
We define here q-Gamow states corresponding to Tsallis' q-statistics. We compute for them their norm, mean energy value an the q-analogue of the Breit-Wigner distribution (a q-Breit-Wigner).
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. This is a review of recent developments in the subject.
Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…
We define the algebra of Colombeau generalized functions on the space of generalized points of {\mathbb R}^d which naturally contains the tempered generalized functions. The subalgebra of \mathscr{S}-regular generalized functions of this…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
For a set of nonnegative integers $A$, denote by $R_{A}(n)$ the number of unordered representations of the integer $n$ as the sum of two different terms from $A$. In this paper we partially describe the structure of the sets, which have…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
A weight function which $q$-generalizes the ground state wave function of the multi-component Calogero-Sutherland quantum many body system is introduced. Conjectures, and some proofs in special cases, are given for a constant term identity…
We study flat deformations of quotients of a polynomial algebra in a class of graded commutative associative algebras. Functional equations and their solutions in terms of theta functions play important role in these studies. An analog of…
In this work we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on shell approach for the scattering matrix, commonly…
Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor and so on can be disclosed by investigating the state of material systems such as thermodynamic and gas…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
The aim of this work is to study the existence of mean values of observables for infinite-particle systems. Using solutions of the initial value problems to the BBGKY hierarchy and to its dual, we prove the local, in time, existence of the…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…