Spectral theory of quantum systems with exotic symmetries

Project funded by Swedish Research Council (Project grant), grant 2013-04734_VR. Participating organisations named by the source: KTH, Royal Institute of Technology. Funded amount: SEK 3,200,000, as stated by the source. Runs 2014-01-01 to 2017-12-31. Keywords: Naturvetenskap, Natural Sciences, Matematik, Mathematics, Matematisk analys, Mathematical Analysis. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-06); national funding data, not CORDIS. Abstract given by the source: Within the field of quantum physics, certain relatively recent and unconventional classes of symmetries pose a challenge for rigorous mathematical modeling. The aim of this research project is to develop new mathematical tools and techniques to study the spectrum, structure and geometry of quantum mechanical systems with supersymmetry or other exotic symmetries such as intermediate and fractional particle statistics, as well as other models with similar features arising in mathematical physics. The project is split into two main parts with the aim to solve specific questions concerning: A. Intermediate particle statistics and anyons, and B. Supersymmetric matrix models. The mathematical tools involved include methods from analysis such as functional inequalities and variational methods, topological methods such as index theory, as well as algebraic and representation theoretic methods. A better understanding of the spectral theoretic aspects of such quantum systems could lead to significant progress within fundamental as well as applied physics, in particular high-energy and condensed matter physics.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Swedish Research Council. Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The project "Spectral theory of quantum systems with exotic symmetries" was funded by the Swedish Research Council with SEK 3,200,000 from 2014 to 2017. It aims to develop mathematical tools for studying quantum systems with unconventional symmetries. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.