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# Special Issue "Mathematical Physics and Symmetry"

A special issue of *Symmetry* (ISSN 2073-8994).

Deadline for manuscript submissions: **closed (30 April 2019)**.

## Special Issue Editor

Department of Mathematics, 14 MLH, The University of Iowa, Iowa City, IA 52242-1419, USA
Fax: +1 319 335 0627 Interests: mathematical physics; Euclidean field theory; reflection positivity; representation theory; operators in Hilbert space; harmonic analysis; fractals; wavelets; stochastic processes; financial mathematicsSpecial Issues and Collections in MDPI journals |

## Special Issue Information

Dear Colleagues,

Starting with key ideas on reflection positivity in quantum physics, the subject has moved in a number of other directions, including the study of stochastic processes that appear in the representation theory of Lie groups. Motivated by reflection symmetries in Lie groups, there is a new trend in the study of representation theoretic aspects of reflection positivity: reflection positive Markov processes indexed by Lie groups, measures on path spaces, and invariant Gaussian measures in spaces of distribution vectors. This provides new constructions of reflection positive unitary representations. Since early work in mathematical physics, starting in the 1970s, and initiated by A. Jaffe, and by K. Osterwalder and R. Schrader, the subject of reflection positivity has had an increasing influence on both non-commutative harmonic analysis, and on duality theories for spectrum and geometry. In its original form, the Osterwalder-Schrader idea served to link Euclidean field theory to relativistic quantum field theory. It has been remarkably successful, especially in view of the abelian property of the Euclidean setting, contrasted with the non-commutativity of quantum fields. Osterwalder-Schrader and reflection positivity have also become a powerful tool in the theory of unitary representations of Lie groups.

Prof. Palle E.T. 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. *Symmetry* is an international peer-reviewed open access monthly 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 1400 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

- Reflection positivity
- Quantum physics
- Representations
- Lie groups
- Gaussian measures
- Osterwalder-Schrader