Path integrals and perturbation theory for stochastic processes

• Autor(a) principal: Dickman,Ronald
• Data de Publicação: 2003
• Outros Autores: Vidigal,Ronaldo
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Brazilian Journal of Physics
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332003000100005

We review and extend the formalism introduced by Peliti, that maps a Markov process to a path-integral representation. After developing the mapping, we apply it to some illustrative examples: the simple decay process, the birth-and-death process, and the Malthus-Verhulst process. In the first two cases we show how to obtain the exact probability generating function using the path integral. We show how to implement a diagrammatic perturbation theory for processes that do not admit an exact solution. Analysis of a set of coupled Malthus-Verhulst processes on a lattice leads, in the continuum limit, to a field theory for directed percolation and allied models.