GRG Golden Oldie: Lichnerowicz (1964)

© SpringerLichnerowicz, A., Republication of: Propagators, commutators and anti-commutators in general relativity, Gen Relativ Gravit (2018) 50: 145.

Golden Oldie

First Online: 16 October 2018


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.

Editorial Note:

An editorial note (free access) to this paper written by Giampiero Esposito and a brief biography by M. A. H. MacCallum can be found in this issue preceding this Golden Oldie and online via

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.

GRG Golden Oldies:

The Golden Oldies series of the journal General Relativity and Gravitation reprints important papers in general relativity theory that were published 30 or more years ago and are either hard to get hold of, or were originally printed in a language other than English.