Mode d'emploi de la théorie constructive des champs bosoniques (A user's guide to bosonic constructive field theory)

Abstract

We develop in this article the principal constructive arguments used in quantum field theory, limiting us to bosonic theories, for which there does not exist any recent general presentation. The article is primarily written for mathematicians or mathematical physicists knowing the basic arguments of quantum field theory, and desiring to discover a general framework in which they can be made rigorous. It also provides a glimpse of a recent series of articles \cite{MagUnt1,MagUnt2} whose aim is to give a constructive definition of rough paths and fractionary stochastic calculus.

44 pages, 4 figures. Paper in French, but with an essential French-English glossary

References in corpus (4)

• Constructive ${\varphi }^4$ field theory without tears
• A Lévy area by Fourier normal ordering for multidimensional fractional Brownian motion with small Hurst index
• A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index $H<1/4$
• A renormalized rough path over fractional Brownian motion