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.
Description:
This abstract was presented
at the ‘Studentesimposium
in die Natuurwetenskappe
2011’, presented under
the protection of the Suid-
Afrikaanse Akademie vir
Wetenskap en Kuns. The
symposium was held at the
University of South Africa on
27–28 October 2011.