Computational Path Integration

[Trajito]

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?

 

[Trajito]

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.