Special Issue "Mathematical physics"
A special issue of Mathematics (ISSN 2227-7390).
Deadline for manuscript submissions: closed (31 May 2015).
Interests: mathematical physics; Euclidean field theory; reflection positivity; representation theory; operators in Hilbert space; harmonic analysis; fractals; wavelets; stochastic processes; financial mathematics
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Mathematical physics dates back a long time, but in the 20th century it has come to center around mathematical methods used in quantum theory, both relativistic and non-relativistic; and including such major areas as quantum field theory, and quantum statistical mechanics. Each of these areas in turn entails notions of dynamics, dynamical systems, scattering theory, the study of interactions, and rigorous theories of phase transition. Because of the foundations of quantum theory, and the framework suggested by John von Neumann and Paul Dirac, the problems and the models studied in mathematical physics rely on the theory linear operators in Hilbert space, and on algebras of operators. Of more recent vintage is a set of advances in quantum information theory, and associated qubit (or quantum bit) algorithms. Related to this is the theory of quantum measurement problems. Within quantum field theories, there are the axiom systems of Wightman fields, as well of Euclidean fields; and both areas relying on measures in path-space; as well as consideration of unitary representations and their harmonic analysis and spectral theory; as well as on analytic continuation tools. Only a year ago, we saw a solution to the Kadison-Singer problem, which also has its roots in Dirac's formulation of quantum theory; although it turns out to also have other striking implications, even outside mathematical physics proper.
Prof. Dr. Palle Jorgensen
Manuscript Submission Information
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- Quantum fields
- Euclidean fields
- statistical mechanics
- mathematical methods in physics
- measures on function spaces
- use of algebras of operators in math phys
- use of representations of Lie groups in physics
- reflection positivity and representations
- Schrödinger operators
- approaches via Feynman and Kac
- spectral analysis
- Monte-Carlo methods