A smooth introduction to the wavefront set
Abstract
The wavefront set of a distribution describes not only the points where the distribution is singular, but also the ‘directions’ of the singularities. 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 stepbystep 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2014
 DOI:
 10.1088/17518113/47/44/443001
 arXiv:
 arXiv:1404.1778
 Bibcode:
 2014JPhA...47R3001B
 Keywords:

 Mathematical Physics
 EPrint:
 29 pages, 7 figures