相关论文: Algebras of unbounded operators and physical appli…
In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
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…
The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
Several quantum systems have been used in the last few years to extend supersymmetry. In this paper we show all this systems fit into the picture of what we call "Number Operator Algebras".
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
Quantum algebra of differential operators are studied
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
Some ideas about phenomenological applications of quantum algebras to physics are reviewed. We examine in particular some applications of the algebras $U_ q (su_2)$ and $U_{qp}({\rm u}_2)$ to various dynamical systems and to atomic and…
We define and investigate properties of universal operator algebras of directed graphs. Results include free products decomposition and continuity of the construction with respect to direct limits. Lastly we prove some K-theoretic results…
The input and output algebras of an infinite qubit system and their representations are described.
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
Lecture notes to a one-term course on operator algebras and their application in physics. Very brief and basic introduction to the subject of Banach- and C-star algebras complemented with their appearance in physics. The course is intended…
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…