Scattering in Algebraic Approach to Quantum Theory—Associative Algebras

Algebraic Quantum Field Theory and Operator Algebras

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 algebraic quantum field theory " would be equally fitting. Besides a presentation of the framework and the main results of local quantum physics these notes may s...

Noncommutative Algebraic Geometry: from pi-algebras to quantum groups

The main purpose of this paper is to provide a survey of different notions of algebraic geometry, which one may associate to an arbitrary noncommutative ring R. In the first part, we will mainly deal with the prime spectrum of R, endowed both with the Zariski topology and the stable topology. In the second part we focus on quantum groups and, in particular, on schematic algebras and show how a ...

Algebraic approach to interacting quantum systems

We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different (spinparticle-gauge) languages by means of exact mappings (isomorphisms) that we name dictionaries and prove a fundamental theorem establishing when two arbitrary languag...

Effective algebraic analysis approach to linear systems over Ore algebras

An Algebraic Approach to States on MV-algebras

In this paper we will introduce the variety of state MV-algebras by enlarging the language of MV-algebras with an unary operator σ, and by adding equations ensuring σ to satisfy some basic properties of a state on an MV-algebra in the sense of [4]. The main result of this paper says us that there is a standard way to define a state MV-algebra starting from a state on an MV-algebra and vice-vers...