Introduction to Path Integral Methods

Lawrence S. Schulman

K.K. Thornber

Nicola Fabiano

Introduction/purpose: Starting from the Hamiltonian an alternative description of quantum mechanics has been given, based on the sum of all possible paths between an initial and a final point. Methods: Theoretical methods of mathematical physics. Integral method based on the path integral. Results: The method and concepts of the path integral could be applied to other branches of physics, not limited to quantum mechanics. Conclusions: The Path Integral approach gives a global description of fields, unlike the usual Lagrangian approach which is a local description of fields.

Marise J. E. Westbroek, Peter R. King, Dimitri D. Vvedensky +1 more

We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the existence of autocorrelations and the calculation of reliable errors. The over-relaxation technique is presented as a way to counter strong autocorrelations. The simulation methods can be extended to compute observables for path integrals in other settings.

Marise J. E. Westbroek, Peter R. King, Dimitri D. Vvedensky +1 more

We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the existence of autocorrelations and the calculation of reliable errors. The over-relaxation technique is presented as a way to counter strong autocorrelations. The simulation methods can be extended to compute observables for path integrals in other settings.