KTH/Nordita/SU seminar in Theoretical Physics

Geometry and Topology in the Matrix Regularization of Membrane Theory

by Dr Joakim Arnlind (Linköping University)



Just as String theory is based on the principle that a moving string should sweep out a minimal area in space-time, Membrane theory demands that a membrane (i.e. a surface) should sweep out a minimal volume. In String theory, one has by now access to a large amount of information about the classical and quantum system. In comparison, almost nothing is known for membranes; even the classical equations of motion are not easy to handle. So far, the only path to the corresponding quantum system has gone through a "matrix regularization". More specifically, functions are replaced by sequences of matrices (of increasing dimension) in such a way that the physically important Poisson bracket corresponds to commutators of matrices. It turns out that this procedure is not only directly relevant for physics, but is also of separate interest from a purely mathematical point of view. In this talk I will give a short introduction to this way of regularizing by matrices, and then present some recent results on how geometry can be encoded in matrix sequences.