Numéro
J. Phys. France
Volume 46, Numéro 9, septembre 1985
Page(s) 1469 - 1483
DOI https://doi.org/10.1051/jphys:019850046090146900
J. Phys. France 46, 1469-1483 (1985)
DOI: 10.1051/jphys:019850046090146900

Path integral approach to birth-death processes on a lattice

L. Peliti

Dipartimento di Fisica, Universita « La Sapienza », Piazzale Aldo Moro 2, I-00185 Roma and Gruppo Nazionale di Struttura della Materia, Unità di Roma, Roma, Italy


Abstract
The Fock space formalism for classical objects first introduced by Doi is cast in a path integral form and applied to general birth-death processes on a lattice. The introduction of suitable auxiliary variables allows one to formulate random walks with memory and irreversible aggregation processes in a Markovian way, which is treatable in this formalism. Existing field theories of such processes are recovered in the continuum limit. Implications of the method for their asymptotic behaviour are briefly discussed.


Résumé
On donne une formulation par intégrales de chemin du formalisme de Fock pour objets classiques, premièrement introduit par Doi, et on l'applique à des processus généraux de naissance et mort sur réseau. L'introduction de variables auxiliaires permet de donner une forme Markovienne aux lois d'évolution des chemins aléatoires avec mémoire et des processus irréversibles d'agrégation. Les théories des champs existantes pour ces processus sont obtenues dans la limite continue. On discute brièvement des implications de cette méthode pour leur comportement asymptotique.

PACS
0540 - Fluctuation phenomena, random processes, noise, and Brownian motion.
0550 - Lattice theory and statistics (Ising, Potts, etc.).

Key words
lattice theory and statistics -- random processes

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