We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson’s theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a 1 + 1 dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current th...

By using Fink?s identity some new generalizations of Levinson type inequalities for n-convex functions are obtained. In seek applications our results to information theory, based on f-divergence estimates also proven. Moreover, Shannon entropies deduced as well.

Levinson’s Theorem in asymptotic integration of linear differential systems is strengthened in a quantitative way. It is shown that any decay in excess of absolute integrability appears with the remainder.