Nuclear, Particle, Astroparticle and Cosmology (NUPAC) Seminars
Monte Carlo Simulations of Awkward Actions
Presented by David Amdahl (UNM)
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 momenta. The path integral over the momenta is gaussian. Mean values of operators are euclidean path
integrals of the 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 Legrende transformation becomes difficult or so intractable that one can't find the hamiltonian. Even if one finds the hamiltonian, it usually is so complicated that one can't path- integrate over the momenta and get a euclidean path integral with a positive weight function. Monte Carlo simulations don't work when the weight function assumes negative or complex values.
This talk shows how to make path integrals without knowing the Hamiltonian. It also shows how to estimate complex path integrals by combining the Monte Carlo method with numerical integration and a look-up table. This new method lets one estimate the energy densities of
theories that, unlike those with quadratic time derivatives, may have finite energy densities.
2:00 pm, Tuesday, November 27, 2018
PAIS-2540, PAIS
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