Nonabelian Gauge Theories, Nonabelian Fluids and Noncommutative Gravity

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The proposed research will focus on the investigation of nonabelian Gauge Theories, non-Abelian fluids and non-commutative gravity. The PI proposes to use analytic Hamiltonian methods to extract the finite temperature behavior of Yang Mills theory in 3+1 dimensions as well as string breaking. The main tool will be to use a set of gauge invariant matrix variables. The PI will study the quantization of a nonabelian generalization of fluid mechanics that he has developed. The PI will study applications to astrophysics as well as study the quark gluon plasma in out of equilibrium situations. As a final project the PI intends to study theories of noncommutative gravity described by finite dimensional matrices. The main advantage of this approach is to be able to have finite mode approximations to gravity that preserve various invariance requirements.