Studying Quantum Field Theory
Abstract
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations of the quantum mechanical conformal group SU(2,2) in the study of gauge fields and their higher spin generalization. A recent revival of the (Bogolubov-)Epstein-Glaser approach to position space renormalization is reviewed including an application to the calculation of residues of primitively divergent graphs. We end up with an optimistic outlook of current developments of analytic methods in perturbative QFT which combine the efforts of theoretical physicists, algebraic geometers and number theorists.
Cite
@article{arxiv.1311.7258,
title = {Studying Quantum Field Theory},
author = {Ivan Todorov},
journal= {arXiv preprint arXiv:1311.7258},
year = {2013}
}
Comments
28 pages, Extended version of an evening talk at the Conference "Quantum Field Theory, Periods and Polylogarithms", dedicated to David Broadhurst's 65th birthday, Humboldt University, Berlin, June 2012. Updated, Sects. 2 and 5 made the essential part of an invited talk at the Second Bulgarian National Congress of Physics, Sofia, September 2013