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Asymptotic properties of path integral ideals
A Bogojević1, A Balaz, A Belić
1Institute of Physics, P.O. Box 57, 11001 Belgrade, Serbia and Montenegro.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
We introduce the path integral ideal, a novel quantity that enhances the convergence of discrete theories transitioning to the continuum limit. This method classifies theory flow by potential divergence, improving predictions for large time steps.
Area of Science:
- Theoretical Physics
- Mathematical Physics
Background:
- Understanding the transition from discrete to continuum theories is crucial in physics.
- Existing methods for analyzing this flow can face convergence challenges.
Purpose of the Study:
- Introduce and analyze the path integral ideal, a new quantity for discrete-to-continuum theory flow.
- Enhance the convergence of generic discrete theories in the continuum limit.
- Classify theory flow based on potential divergence at spatial infinity.
Main Methods:
- Analysis of the path integral ideal.
- Classification of theory flow by the degree of potential divergence at spatial infinity.
- Study of asymptotic behavior of path integral ideals.
Main Results:
- The path integral ideal significantly increases the convergence of discrete theories.
- Theory flow is classified based on potential divergence at spatial infinity.
- Dominant terms in the effective potential determining large discrete time step behavior are isolated.
Conclusions:
- The path integral ideal provides a powerful tool for analyzing discrete-to-continuum transitions.
- Understanding potential divergence is key to predicting theory behavior in the continuum limit.
- The identified dominant terms offer insights into the long-time behavior of generic theories.