Computational Path Integration

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SUMMARY

The discussion centers on the effectiveness of various Monte Carlo algorithms for Feynman path integrals, specifically evaluating the VEGAS algorithm from the GNU Scientific Library. While VEGAS is useful for multi-dimensional integrals, it produces significant errors with Gaussian integrals. The Metropolis-Hastings algorithm is confirmed as a suitable alternative for high-dimensional integrals, with Gibbs sampling also being a common method. The Metropolis-Hastings algorithm is noted for its complexity and advanced nature compared to Gibbs sampling.

PREREQUISITES
  • Understanding of Feynman path integrals
  • Familiarity with Monte Carlo methods
  • Knowledge of the VEGAS algorithm from the GNU Scientific Library
  • Basic concepts of Markov chain Monte Carlo techniques
NEXT STEPS
  • Research the implementation of the Metropolis-Hastings algorithm in computational physics
  • Explore Gibbs sampling techniques for high-dimensional integrals
  • Study the limitations of the VEGAS algorithm with Gaussian integrals
  • Learn about alternative Monte Carlo algorithms for path integrals
USEFUL FOR

Physicists, computational scientists, and researchers involved in numerical integration and Monte Carlo simulations, particularly those focusing on Feynman path integrals and high-dimensional integrals.

Trajito
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Hello to all,

To take Feynman path integrals, which Monte Carlo algorithm do you think is best to use? I tried VEGAS algorithm as it is in GNU Scientific Library. It is pretty useful for many kinds of multi-dimensional integrals but since the path integral formulation includes Gaussian integrals, it gives really huge errors (I don't know why it isn't suitable for the Gaussians). So, do you think Metropolis works?
 
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The answer was "yes." When calculating every kind of very high dimensional integrals, Markov chain Monte Carlo methods are widely employed. Two most common of these are Gibbs sampling and the Metropolis-Hastings algorithm. Both have advantages; the latter is, as far as I see, much more complicated and much more advanced.
 

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