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Republication of: Propagators, commutators and anti-commutators in general relativity

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Abstract

This is an English translation of A. Lichnerowicz’ 1964 paper “Propagateurs, commutateurs et anticommutateurs en relativité générale”. It was based on lectures at a Les Houches school, and gave a classic summary of the author’s work on quantum propagators in curved space-times, introducing tensorial and spinorial propagators which generalise the flat space propagators of Jordan and Pauli. It gives the quantum commutators for the Maxwell and Dirac fields and for perturbations of the gravitational field, and numerous intermediate formulae. The results are basic to quantum field theory in curved space-times. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by G. Esposito and by a brief biography written by M. A. H. MacCallum.

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Author notes

  1. A. Lichnerowicz (Deceased December 11, 1998).

Authors and Affiliations

  1. Collège de France, Paris, France

    André Lichnerowicz

Authors
  1. André Lichnerowicz
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Correspondence to André Lichnerowicz.

Additional information

An editorial note to this paper and a biography can be found in this issue preceding this Golden Oldie and online via https://doi.org/10.1007/s10714-018-2432-y.

Original paper: A. Lichnerowicz, Propagateurs, commutateurs et anticommutateurs en relativité générale. In “Relativity, Groups and Topology” ed. C. DeWitt and B. DeWitt, Blackie and Son (1964), pp. 823–861.

Translated and republished by the kind permission of Jérôme Lichnerowicz. We are grateful to Profs. Pierre Cartier, Yvette Kosmann-Schwarzbach and Daniel Sternheimer for assistance in locating Jérôme Lichnerowicz.

Translated by Giampiero Esposito, E-mail: giampiero.esposito@na.infn.it.

Editorial responsibility: M. A. H. MacCallum, e-mail: m.a.h.maccallum@qmul.ac.uk.

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Lichnerowicz, A. Republication of: Propagators, commutators and anti-commutators in general relativity. Gen Relativ Gravit 50, 145 (2018). https://doi.org/10.1007/s10714-018-2433-x

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  • DOI: https://doi.org/10.1007/s10714-018-2433-x

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