Formulating the Kramers Problem in Field Theory

The Kramers problem aims at deriving the rate at which a Brownian particle
escapes from a potential well. In this talk, I will define and derive the
Kramers escape rate for a scalar field, due to thermal fluctuations, and
discuss the applications for cosmology and other areas. In the presence of
such fluctuations, there is a non-vanishing probability for a field,
initially homogeneously located at a minimum of its potential, to escape
from the well. I will start with a review of the simpler problem of the
escape of a classical particle due to random forces. Then, I will discuss
the difficulties associated with a well-defined formulation of an escape
rate for a field and how these can be overcome. I will attempt to provide
a definition of the Kramers problem for a scalar field and present a
method to obtain the rate. Finally, I will conclude with some applications
of the formalism not only in cosmology but also in areas including
lattice gauge theory and condensed matter physics.

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