INVESTIGADORES
CALZETTA Esteban Adolfo
artículos
Título:
Stochastic dynamics of correlations in quantum field theory: From the Schwinger-Dyson to Boltzmann-Langevin equation
Autor/es:
BEI-LOK HU; ESTEBAN CALZETTA
Revista:
PHYSICAL REVIEW D - PARTICLE AND FILDS
Editorial:
APS
Referencias:
Año: 1999 vol. 61 p. 1 - 22
ISSN:
0556-2821
Resumen:
The aim of this paper is twofold: to probe the statistical mechanical
properties of interacting quantum fields, and to provide a field
theoretical justification for a stochastic source term in the Boltzmann
equation. We start with the formulation of quantum field theory in terms
of the set of Schwinger-Dyson equations for the correlation functions,
which we describe by a closed-time-path master (n=∞PI)
effective action. When the hierarchy is simply truncated to a certain
order, one obtains the usual closed system of correlation functions up
to that order, and from the nPI
effective action, a set of time-reversal invariant equations of motion.
(This is the Dyson equation, the quantum field theoretical parallel of
the collisionless Boltzmann equation.) But when the effect of the higher
order correlation functions is included through a causal factorization
condition (such as the molecular chaos assumption in Boltzmann?s theory)
called slaving, the dynamics of the lower order correlations shows
dissipative features, as familiar in the usual (dissipative yet
noiseless) Boltzmann equation, the field-theoretical version of which
being the dissipative Dyson equations. We show that a
fluctuation-dissipation relation should exist for such effectively open
systems, and use this fact to show that a stochastic term, which
explicitly introduces quantum fluctuations in the lower order
correlation functions, necessarily accompanies the dissipative term.
This leads to a stochastic Dyson equation, which is the quantum field
theoretic parallel of the classical Boltzmann-Langevin equation,
encompassing both the dissipative and stochastic dynamics of correlation
functions.