Classical dynamics of quantum fluctuations

Details Classical dynamics of quantum fluctuations Classical dynamics of quantum fluctuations

2002-07-28

arxiv.org/abs/hep-th/0207251v2

Phys.Rev. D67 (2003) 025010

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, no figures. Two sections added

Scientific paper

10.1103/PhysRevD.67.025010

It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with constrained initial conditions. We call such paths "pseudoclassical" paths and use them to define the dynamics of quantum fluctuations. Every physical observable is assigned a time-dependent value on each path in a way that respects the uncertainty principle, but in consequence, some of the standard algebraic relations between quantum observables are not necessarily fulfilled by their time-dependent values on paths. We define "collective observables" which depend on a large number of independent degrees of freedom, and show that the dynamics of their quantum fluctuations can be described in terms of unconstrained classical stochastic processes without reference to any additional external system or to an environment. Our analysis can be generalized to states other than the vacuum. Finally, we compare our formalism to the formalism of coherent states, and highlight their differences.

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