PIRSA:08040046

A unifying view of graph theory in quantum field theory

Kempf, A. (2008). A unifying view of graph theory in quantum field theory . Perimeter Institute. https://pirsa.org/08040046

Kempf, Achim. A unifying view of graph theory in quantum field theory . Perimeter Institute, Apr. 28, 2008, https://pirsa.org/08040046 

          @misc{ pirsa_PIRSA:08040046,
            doi = {10.48660/08040046},
            url = {https://pirsa.org/08040046},
            author = {Kempf, Achim},
            keywords = {Quantum Information},
            language = {en},
            title = {A unifying view of graph theory in quantum field theory },
            publisher = {Perimeter Institute},
            year = {2008},
            month = {apr},
            note = {PIRSA:08040046 see, \url{https://pirsa.org}}
          }

Achim Kempf University of Waterloo

Talk numberPIRSA:08040046
DOI10.48660/08040046
Collection
Talk Type Conference
Subject

Abstract

A fundamental theorem of quantum field theory states that the generating functionals of connected graphs and one-particle irreducible graphs are related by Legendre transformation. An equivalent statement is that the tree level Feynman graphs yield the solution to the classical equations of motion. Existing proofs of either fact are either lengthy or are short but less rigorous. Here we give a short transparent rigorous proof. On the practical level, our methods could help make the calculation of Feynman graphs more efficient. On the conceptual level, our methods yield a new, unifying view of the structure of perturbative quantum field theory, and they reveal the fundamental role played by the Euler characteristic of graphs. This is joint work with D.M. Jackson (UW) and A. Morales (MIT)