Particles, Astrophysics, and Nuclear Physics Seminar
How to Compute Some Really Big Determinants – Mass Dependence of Fermion Determinant in an Instanton Background
Professor of Physics
I describe a recent computation of the precise quark mass dependence of the one-loop effective action in an instanton background. Previously, only the extreme small and large mass limits were known for this quantity. Our result interpolates smoothly between these previously known limits. The computational method makes use of the fact that the single instant on background has radial symmetry, so that the computation can be reduced to a sum over partial waves of logarithms of radial determinants, each of which can be computed numerically in an efficient manner. The bare sum over partial waves is divergent and must be regulated and renormalized. The method is general and versatile, and can be applied to many field theoretic computations.
Monday, October 31, 2005
Gant Science Complex