, Volume 75, Issue 4, pp 349-372

The principle of minimal gravitational coupling

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Abstract

The principle of minimal gravitational coupling requires that the total Lagrangian for the field equations of general relativity consist of two additive parts, one part corresponding to the free gravitational Lagrangian and the other part to external source fields in curved spacetime. For source fields characterized by scalars, vectors and two-component spinors we prove that this additive decomposition of the total Lagrangian is an inevitable consequence of certain very general assumptions concerning the Euler-Lagrange expressions arising from the total Lagrangian.

It is a pleasure to thank Professors D. Lovelock and K. Kuchar for their helpful advice in the preparation of this paper. I am also indebted to my friend G. Horndeski for his critical reading of this manuscript.
Communicated by M. M. Schiffer