Asymptotic properties of path integral ideals

2005/09/28 by Aleksandar Bogojević, Aleksandar Bogojevic, Antun Balaž +3 · 15 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Computer science #Convergence (economics) #Cosmology and Gravitation Theories #Divergence (linguistics) #Flow (mathematics) #Geometry #Ideal (ethics) #Infinity #Limit (mathematics) #Mathematical analysis #Mathematics #Path (computing) #Path integral formulation #Physics #advanced mathematical theories #cond-mat.stat-mech #hep-th #physics.comp-ph

paper · pdf · doi:10.1103/physreve.72.036128

published in Physical Review E 72(3), 036128 (American Physical Society) · 4 pages, 1 figure, revtex

arxiv created 2005/09/28 · openalex publication_date 2005/09/28 · arxiv updated 2011/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce and analyze an interesting quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of divergence of the potential at spatial infinity. Studying the asymptotic behavior of path integral ideals we isolate the dominant terms in the effective potential that determine the behavior of a generic theory for large discrete time steps.

Citations

• Generalization of Euler's summation formula to path integrals
• Systematic speedup of path integrals of a genericN-fold discretized theory
• Path integrals in the theory of condensed helium
• Dependence of variational perturbation expansions on strong-coupling behavior: Inapplicability ofδexpansion to field theory

Cited by

• Time-of-flight expansion of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime