Asymptotic expansion of the lattice scalar propagator in coordinate space

Abstract

The asymptotic expansion of the massive scalar field propagator on a n-dimensional lattice is derived. The method used is based on the evaluation of the asymptotic expansion of the modified Bessel function $I_{\nu }({\nu }^2\beta )$ as the order $\nu$ grows to infinity.

Comments: 13 pages, 2 figures. Updated version (accepted for publication on Phys. Lett. B) includes evaluation of the one-loop mass renormalization in lattice lambda phi^4 theory