Feynman integrals and periods in configuration spaces

Creators: Ceyhan, Özgür; Marcolli, Matilde

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Abstract

We describe differential forms representing Feynman amplitudes in configuration spaces of Feynman graphs, and regularization and evaluation techniques, for suitable chains of integration, that give rise to periods of mixed Tate motives.

Additional Information

(Submitted on 15 Jul 2012 (v1), last revised 26 Oct 2012 (this version, v2). Parts of this work have been carried out during visits of the first author to the California Institute of Technology, the Institut des Hautes Études Scientifiques and the Max Planck Institut für Mathematik. We thank these institutions for their support. The second author acknowledges support from NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. The authors thank Paolo Aluffi and Spencer Bloch for many useful conversations. The first author's son, Uzay, was diagnosed with neuroblastoma, at the time when we were in the early stages of this project. His doctor, Tanju Başarir Özkan, not only saved Uzay with her exceptional professional skills, but also gave constant personal support, so that Ö.C. could return to work and continue the project. This paper is dedicated to her, to express the author's deepest gratitude: Ellerin dert görmesin Tanju abla.

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