Approximation methods for large-N matrix models
Dr. Govind Krishnaswami
Utrecht University, The Netherlands.
Matrix models are toy-models for gluon dynamics in quantum non-abelian gauge theories, such as the physically relevant QCD. The limit as the matrices become large is a `classical' limit and expected to be a good approximation. However, the problem of determining correlations of large-N matrix models is itself very difficult and requires further approximations. We discuss a few such methods based on algebraic and probabilistic structures of large-N matrix models. A variational approach is presented, which involves the confluence of ideas on the entropy of operator-valued random variables and cohomology of automorphism groups of free algebras. Another technique seeks to exploit ideas from deformation quantization to approximately solve the equations of matrix models.