Perturbative classical and quantum field theory

Details Perturbative classical and quantum field theory Perturbative classical and quantum field theory

2006-03-06

arxiv.org/abs/math-ph/0603014v1

Physics

Mathematical Physics

12 pages, 2 figures

Scientific paper

In a first part we study the phi^{p+1}--field theory from the classical point of view. Using Butcher series we compute explicitly the perturbative expansion of the solutions and we prove that this expansion converges if the coupling constant is small enough. Then we show that we can formally recover the Heisenberg's interacting quantum field directly from this expansion. In other words we write the Heisenberg interacting field as a Butcher series.

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