Fast way to compute functional determinants of radially symmetric partial differential operators in general dimensions
Abstract
Recently the partialwave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive explicitly radialWKB series in the angular momentum cutoff for d=2, 3, 4, and 5 (d is the spacetime dimension), which has uniform validity irrespectively of any specific values assumed for other parameters. Utilizing this series, precision evaluation of the renormalized functional determinant is possible with a relatively small number of low partialwave contributions determined separately. We illustrate the power of this scheme in a numerically exact evaluation of the prefactor (expressed as a functional determinant) in the case of the false vacuum decay of 4D scalar field theory.
 Publication:

Physical Review D
 Pub Date:
 June 2008
 DOI:
 10.1103/PhysRevD.77.125033
 arXiv:
 arXiv:0805.0079
 Bibcode:
 2008PhRvD..77l5033H
 Keywords:

 12.38.t;
 11.15.q;
 11.15.Ha;
 Quantum chromodynamics;
 Gauge field theories;
 Lattice gauge theory;
 High Energy Physics  Theory
 EPrint:
 28 pages, 2 figures