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.

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

References in corpus (13)

• Motivic Amplitudes and Cluster Coordinates
• Event shapes in N=4 super-Yang-Mills theory
• A note on three-point functions of conserved currents
• On Conformal Field Theories With Extremal a/c Values
• Single-valued periods and multiple zeta values
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• Constraining conformal field theories with a higher spin symmetry in d=4
• Vertex Algebras in Higher Dimensions and Globally Conformal Invariant Quantum Field Theory
• The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
• Globally conformal invariant gauge field theory with rational correlation functions
• Harmonic bilocal fields generated by globally conformal invariant scalar fields
• Feynman amplitudes and Landau singularities for 1-loop graphs
• Renormalization theory of Feynman amplitudes on configuration spaces