Path Integrals for Fermions and Bosons

J. T. Devreese, L. F. Lemmens, F. Brosens

L. F. Novikov

R. Shankar

Tom Kim

I set up the path integral formalism to study interacting bosonic gases, binary boson-fermion mixtures, and fermionic superconductors. The large-N theory is applied to bosonic interactions. The corresponding auxiliary field theory is applied to fermionic interactions. Using the thermodynamic quantities obtained by evaluating the path integral, I map out the phase boundaries. For fermionic superconductors, the path integral method reproduces well-known methods that were developed previously.

Yunuo Xiong, Hongwei Xiong

In this article we develop a general method to numerically calculate physical properties for a system of anyons with path integral molecular dynamics. We provide a unified method to calculate the thermodynamics of identical bosons, fermions, and anyons. Our method is tested and applied to systems of anyons, bosons, and fermions in a two-dimensional harmonic trap. We also consider a method to calculate the energy for fermions as an application of the path integral molecular dynamics to simulate the anyon model.