A smooth introduction to the wavefront set

Christian Brouder (1) , Nguyen Viet Dang (2) , Frédéric Hélein (2)

1 IMPMC - Institut de minéralogie, de physique des matériaux et de cosmochimie
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

The wavefront set provides a precise description of the singularities of a distribution. Because of its ability to control the product of distributions, the wavefront set was a key element of recent progress in renormalized quantum field theory in curved spacetime, quantum gravity, the discussion of time machines or quantum energy inequalitites. However, the wavefront set is a somewhat subtle concept whose standard definition is not easy to grasp. This paper is a step by step introduction to the wavefront set, with examples and motivation. Many different definitions and new interpretations of the wavefront set are presented. Some of them involve a Radon transform.

Mots clés: wave front set; quantum field theory; renormalization; microlocal analysis

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Analyse fonctionnelle [math.FA]

Christian Brouder, Nguyen Viet Dang, Frédéric Hélein. A smooth introduction to the wavefront set. 2014. ⟨hal-00971282⟩