Idea of Path integral Monte Carlo

Exchange of Fermi particles

Illustration of the Fermionic exchanges: Shown are 5 non-interacting electrons in a two-dimensional plane in real space. Each line (color) corresponds to the "trajectory" (or probability density) of one electron.
Left figure: neglecting spin. Thick dots are initial and final point of the trajectory (they coincide)
right figure: with spin included. Notice that different lines ("polymers") are now connected - this is fermionic exchange in the path integral picture.

Formulas and simulation by Alexei Filinov, 2000

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