18,593 research outputs found
The induced Chern-Simons term at finite temperature
It is argued that the derivative expansion is a suitable method to deal with
finite temperature field theory, if it is restricted to spatial derivatives
only. Using this method, a simple and direct calculation is presented for the
radiatively induced Chern-Simons--like piece of the effective action of
(2+1)-dimensional fermions at finite temperature coupled to external gauge
fields. The gauge fields are not assumed to be subjected to special
constraints, and in particular, they are not required to be stationary nor
Abelian.Comment: 5 pages, REVTEX, no figure
Representation of Complex Probabilities
Let a ``complex probability'' be a normalizable complex distribution
defined on . A real and positive probability distribution , defined
on the complex plane \C^D, is said to be a positive representation of
if , where is any
polynomial in and its analytical extension on \C^D. In this
paper it is shown that every complex probability admits a real representation
and a constructive method is given. Among other results, explicit positive
representations, in any number of dimensions, are given for any complex
distribution of the form Gaussian times polynomial, for any complex
distributions with support at one point and for any periodic Gaussian times
polynomial.Comment: REVTeX, 15 pages, no figures, uuencode
Project 150: High School is Tough Enough
https://digitalscholarship.unlv.edu/educ_sys_202/1117/thumbnail.jp
Representation of complex probabilities and complex Gibbs sampling
Complex weights appear in Physics which are beyond a straightforward
importance sampling treatment, as required in Monte Carlo calculations. This is
the well-known sign problem. The complex Langevin approach amounts to
effectively construct a posi\-tive distribution on the complexified manifold
reproducing the expectation values of the observables through their analytical
extension. Here we discuss the direct construction of such positive
distributions paying attention to their localization on the complexified
manifold. Explicit localized repre\-sentations are obtained for complex
probabilities defined on Abelian and non Abelian groups. The viability and
performance of a complex version of the heat bath method, based on such
representations, is analyzed.Comment: Proceedings of Lattice 2017 (The 35th International Symposium on
Lattice field Theory). 8 pages, 4 figure
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