Related papers: Some Aspects of Operator Algebras in Quantum Physi…
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…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
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…
It is shown how a C*-algebra representation of the transformations of a physical system can be derived from two operational postulates: 1) the existence of dynamically independent systems}; 2) the existence of symmetric faithful states.…
A C*-algebra formulation of Quantum Mechanics is derived from purely operational axioms in which the primary role is played by the "transformations" that the system undergoes in the course of an "experiment". The notion of the {\em adjoint}…
The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
In this article we give a short and informal overview of some aspects of the theory of C*- and von Neumann algebras. We also mention some classical results and applications of these families of operator algebras.
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of…
I contrast the profound differences in the ways in which algebra and analysis are used in physics. In particular I discuss the fascinating phenomenon that theoretical physicists devote almost all their efforts to algebraic problems even…