NC Fuzzy Gauge Field

Noncommutative geometry was proposed earlier than renormalization as a possible way to eliminate ultraviolet divergences in quantum field theories. On the other hand quantum field theories on noncommutative spaces are generally unknowm beyond the one-loop approximation. The main focus of this proposal is the construction of a new nonperturbative method for chiral gauge theories based on the fuzzy tw-speres and their Cartesian products. More precisely we will use Monte CArlo numerical simulations to a) determine the phase structure of 2-dimensional noncommutative fuzzy Yang-Mills Theory, and b) to solve the noncommutative fuzzy Schwinger-model. This will provide a crucial step towards understanding chiral gauge theories on infinite dimensional noncommutative Moyal-Weyl spaces. But it will also lay the foundation for the study of ordinary QCD in two and four dimensions using fuzzy approximations.