General Path Integrals Properties

There are three flmdamental properties most useful for path integral calculations (Dittrich Reuter, 1994). 

Quantum Nanochemistry-Volume I Quantum Theory and Observability 

Secondly, from the Huygens principle Eq. (4.46) there is abstracted also the limiting delta Dirac-flmction for a propagator connecting two space events simultaneously  

This property is often used as the analytical check once a path integral propagator is calculated for a given system. 

Thirdly, and perhaps most practically, one would like to be able to solve the path integrals, say with canonical Lagrangian form (4.32), in more direct way than to consider all multiple integrals involved in the measure (4.28). 

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This review is a brief update of the recent progress in the attempt to calculate properties of atoms and molecules by stochastic methods which go under the general name of quantum Monte Carlo (QMC). Below we distinguish between basic variants of QMC variational Monte Carlo (VMC), diffusion Monte Carlo (DMC), Green s function Monte Carlo (GFMC), and path-integral Monte Carlo (PIMC). 

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