Conference Abstract: Studentesimposium in die Natuurwetenskappe 2011

A noncommutative sigma model

Mauritz van den Worm
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie | Vol 32, No 1 | a423 | DOI: https://doi.org/10.4102/satnt.v32i1.423 | © 2013 Mauritz van den Worm | This work is licensed under CC Attribution 4.0
Submitted: 25 June 2013 | Published: 08 July 2013

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Mauritz van den Worm, Department of Physics, University of Pretoria, South Africa


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Abstract

We replace the classical string theory notions of mapping between parameter space and world-time with noncommutative tori mapping between these spaces. The dynamics of mappings between different noncommutative tori are studied and noncommutative versions of the Polyakov action and the Euler-Lagrange equations are derived. The quantum torus is studied in detail, as well as C*-homomorphisms between different quantum tori. A finite dimensional representation of the quantum torus is studied, and the partition function and other path integrals are calculated. At the end we prove existence theorems for mappings between different noncommutative tori.

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