# Special Issue "Mathematical physics"

A special issue of *Mathematics* (ISSN 2227-7390).

Deadline for manuscript submissions: **closed (31 May 2015)**.

## Special Issue Editor

**Interests:**mathematical physics; Euclidean field theory; reflection positivity; representation theory; operators in Hilbert space; harmonic analysis; fractals; wavelets; stochastic processes; financial mathematics

Special Issues, Collections and Topics in MDPI journals

## Special Issue Information

Dear Colleagues,

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

*Guest Editor*

**Manuscript Submission Information**

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. *Mathematics* is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

## Keywords

- 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
- approximation
- Monte-Carlo methods