Asymptotic Properties of Path Integral Ideals

Abstract

We introduce and analyze a new 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.

4 pages, 1 figure, revtex

References in corpus (3)

• Generalization of Euler's Summation Formula to Path Integrals
• Systematic Speedup of Path Integrals of a Generic $N$-fold Discretized Theory
• Jaggedness of Path Integral Trajectories

Cited by in corpus (9)

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• Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator
• Faraday and resonant waves in binary collisionally-inhomogeneous Bose-Einstein condensates
• Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism
• Time-of-flight expansion of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime
• SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach