Pirsa: 15060010 - How to (path) integrate by differentiating


Achim Kempf

Playing this video requires MP4 / H.264 support to be configured and enabled in your browser.

Download link (right click and 'save-as') for playing in VLC or other compatible player.

Download Video


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.

Valid XHTML 1.0!