Twistor connection and conformal gravitation
Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 2, pp. 311-316
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The concept of a local twistor connection is introduced. For the Yang–Mills Lagrangian
of the standard twistor connection (which depends on the metric and its first and second
derivatives) two variational principles are considered: a) variation with respect to the
connection (which leads to 60 equations, of which 50 are shown to vanish identically);
b) variation with respect to the metric (leading to ten equations). It is established that
the extremals of the two variational principles are the same and lead to the vacuum
equations of Hach. A modification of the standard twistor connection to make it depend
on the electromagnetic field tensor as well is proposed. It is shown that in this case
too the two variational principles lead to the same equations – the conformally invariant
equations of Bach in the presence of an electromagnetic field and the free Maxwell
equations.
@article{TMF_1984_60_2_a11,
author = {S. A. Merkulov},
title = {Twistor connection and conformal gravitation},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {311--316},
publisher = {mathdoc},
volume = {60},
number = {2},
year = {1984},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1984_60_2_a11/}
}
S. A. Merkulov. Twistor connection and conformal gravitation. Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 2, pp. 311-316. http://geodesic.mathdoc.fr/item/TMF_1984_60_2_a11/