Nuclear, Particle, Astroparticle and Cosmology (NUPAC) Seminars
Path integrals for awkward actions
Presented by Kevin Cahill, UNM
Time derivatives of scalar fields usually occur quadratically in the action. A simple Legendre transformation then turns the lagrangian into a hamiltonian that is quadratic in the momenta. The path integral over the momenta is gaussian, and the mean values of operators are euclidian path integrals of their classical counterparts weighted by probability distributions.
This familiar framework falls apart when the time derivatives do not occur quadratically. The Legendre transformation becomes difficult or so intractable that one can't find the hamiltonian.
Even if one finds the hamiltonian, it typically is so complicated that one can't path-integrate over the momenta and get a euclidian path integral with a positive weight function.
Recent work with David Amdahl solves both problems. We show how to make path integrals without knowing the hamiltonian and how to estimate complex path integrals by combining the Monte Carlo method with numerical integration and parallel computation. This solution of this sign problem may be broadly useful.
2:00 pm, Tuesday, November 8, 2016
PAIS-2540, PAIS
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