MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in $\phi^4$ Theory

Felix Finster and Jürgen Tolksdorf


Solutions of the classical $\phi^4$-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

MSC Codes:
70Sxx, 81T10, 81Uxx
11.10Ef, 11.10Lm, 11.15Kc
Classical Nonlinear Scattering Problem, Feynman Diagrams, Stochastic Initial Values

Related publications

2012 Repository Open Access
Felix Finster and Jürgen Tolksdorf

Bosonic loop diagrams as perturbative solutions of the classical field equations in \( \phi^4\)-theory

In: Journal of mathematical physics, 53 (2012) 5, p. 052305