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Hyperlogarithms and Periods in Feynman Amplitudes

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Lie Theory and Its Applications in Physics (LT 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 191))

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Abstract

The role of hyperlogarithms and multiple zeta values (and their generalizations) in Feynman amplitudes is being gradually recognized since the mid 1990s. The present lecture provides a concise introduction to a fast developing subject that attracts the interests of a wide range of specialists – from number theorists to particle physicists.

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Notes

  1. 1.

    To cite a few: “Loops and Legs in Quantum Field Theory” Bi-annual Workshop taking place (since 2008) in various towns in Germany; Durham Workshop: “Polylogarithms as a Bridge between Number Theory and Particle Physics” [43]; Research Trimester “Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory”, ICMAT, Madrid, 2014, [39, 40].

  2. 2.

    Nowadays the term is usually associated with the Dedekind \(\eta \)-function \(\eta (\tau ) = e^{i \frac{\pi \tau }{12}} \overset{\infty }{\underset{n=1}{\prod }} \, (1-q^n)\), \(q = e^{2\pi i \tau }\), defined on the upper half plane \(\tau \).

  3. 3.

    We use, following [13, 36], concatenation to the right. Other authors [8, 24] use the opposite convention.

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Acknowledgements

It is a pleasure to thank V. Dobrev for the invitation to Varna and for his careful editorial work. I thank IHES and the Theoretical Physics Department of CERN for hospitality during the preparation of this text. The author’s work is supported in part by Grant DFNI T02/6 of the Bulgarian National Science Foundation.

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Authors and Affiliations

  1. Institut des Hautes Études Scientifiques, 35 Route de Chartres, 91440, Bures-sur-yvette, France

    Ivan Todorov

  2. Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland

    Ivan Todorov

  3. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, 1784, Sofia, Bulgaria

    Ivan Todorov

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Correspondence to Ivan Todorov .

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  1. Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vladimir Dobrev

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Todorov, I. (2016). Hyperlogarithms and Periods in Feynman Amplitudes. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2015. Springer Proceedings in Mathematics & Statistics, vol 191. Springer, Singapore. https://doi.org/10.1007/978-981-10-2636-2_10

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