*Towards the Mathematics of Quantum Field Theory*

#### Posted by Urs Schreiber

Currently I am in Paris, visiting Frédéric Paugam. He is in the process of finishing a book with the title

*Towards the mathematics of quantum field theory.*

This book makes an admirable effort of collecting together for each aspect of QFT the most modern and most elegant mathematical formalism available.

For instance

all smooth geometry is treated with diffeological spaces and generally smooth sheaves

- for example a nice reformulation of the theory of distributions and functional calculus without use of topological vector spaces is given: “functorial analysis”;

smooth infinitesimal and super calculus is thus accordingly treated with the synthetic differential geometry of smooth algebras;

variational calculus of local action functionals is treated with $\mathcal{D}$-jet space technology following Beilinson-Drinfeld’s book;

gauge systems are treated in the derived geometry presented by the BV-BRST complex.

And so on.

Posted at June 21, 2011 10:07 AM UTC
## Re: Towards the Mathematics of Quantum Field Theory

Thanks!