Event

Talk
Membrane equations and matrix regularization
Dr. Joakim Arnlind (MPI Golm)
11 May 2009, 16:30 – 17:30

Membrane theory is a theory aimed at describing the quantum nature of fundamental particles and gravitational forces. 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 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 derived from this principle. 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 an introduction to this way of regularizing by matrices, as well as point out some difficulties and open questions that are addressed within this project.

Related to:

• Joakim Arnlind
• Summer Term 2009