PIRSA:15060010

Video URL

https://pirsa.org/15060010

How to (path) integrate by differentiating

Kempf, A. (2015). How to (path) integrate by differentiating. Perimeter Institute for Theoretical Physics. https://pirsa.org/15060010

Kempf, Achim. How to (path) integrate by differentiating. Perimeter Institute for Theoretical Physics, Jun. 11, 2015, https://pirsa.org/15060010 

          @misc{ scivideos_PIRSA:15060010,
            doi = {10.48660/15060010},
            url = {https://pirsa.org/15060010},
            author = {Kempf, Achim},
            keywords = {Quantum Gravity},
            language = {en},
            title = {How to (path) integrate by differentiating},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2015},
            month = {jun},
            note = {PIRSA:15060010 see, \url{https://scivideos.org/pirsa/15060010}}
          }

Achim Kempf University of Waterloo

Talk numberPIRSA:15060010
DOI10.48660/15060010
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Path integrals are at the heart of quantum field theory. In spite of their covariance and seeming simplicity, they are hard to define and evaluate. In contrast, functional differentiation, as it is used, for example, in variational problems, is relatively straightforward. This has motivated the development of new techniques that allow one to express functional integration in terms of functional differentiation. In fact, the new techniques allow one to express integrals in general through differentiation. These techniques therefore add to the general toolbox for integration and integral transforms such as the Fourier and Laplace transforms. Here, we review some of these results, we give simpler proofs and we add new results, for example, on expressing the Laplace transform and its inverse in terms of derivatives, results that may be of use in quantum field theory, e.g., in the context of heat traces.