Physical Sciences and Mathematics Commons^™

Monte Carlo Simulations Of Awkward Actions, David John Amdahl

Physics & Astronomy ETDs

Time derivatives of scalar fields occur quadratically in textbook actions. A simple Legendre transformation turns the Lagrangian into a Hamiltonian that is quadratic in the momentum. The partition function over the momentum is Gaussian. Mean values of operators are basically euclidian path integrals of their classical counterparts with positive weight functions. Monte Carlo simulations can estimate such mean values. This familiar framework falls apart when the time derivatives do not occur quadratically. The Legendre transformation becomes difficult or so intractable that the Hamiltonian can’t be determined. Even if the Hamiltonian is found, it usually is so complicated that the partition …