Related papers: Subfactors and Mathematical Physics
We consider quantum information tasks in an operator algebraic setting, where we consider normal states on von Neumann algebras. In particular, we consider subfactors $\mathfrak{N} \subset \mathfrak{M}$, that is, unital inclusions of von…
An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory…
Vaughan Jones discovered unexpected connections between Richard Thompson's group and subfactor theory while attempting to construct conformal field theories (in short CFT). Among other this founded Jones' technology: a powerful new method…
Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this…
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
We sketch some connecting relations involving fractional and quantum calculi, fractal structure, thermodynamics, and quantum mechanics.
A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…
We discuss foundation of quantum mechanics (interpretations, superposition, principle of complementarity, locality, hidden variables) and quantum information theory.
This paper reviews connections between physics and computation, and explores their implications. The main topics are computational "hardness" of physical systems, computational status of fundamental theories, quantum computation, and the…
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…
In which a theory of dimension related to the Jones index and based on the notion of conjugation is developed. An elementary proof of the additivity and multiplicativity of the dimension is given and there is an associated trace.…
We survey the salient features and problems of conformal and superconformal mechanics and portray some of its developments over the past decade. Both classical and quantum issues of single- and multiparticle systems are covered.
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
A brief history is given of the factor 2, starting in the most elementary considerations of geometry and kinematics of uniform acceleration, and moving to relativity, quantum mechanics and particle physics. The basic argument is that in all…
We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize…
We review some theoretical and experimental issues in unparticle physics, focusing mainly on collider signatures.