Magnetohydrodynamics: Waves and Shock Waves in Curved Space-Time
For seventy years, we have known that Einstein's theory is essentially a theory of propagation of waves for the gravitational field. Confusion enters, however, through the fact that the word wave, in physics, implies sometimes repetition and sometimes not
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MATHEMATICAL PHYSICS STUDIES
Series Editor:
M. PLATO, Universite de Bourgogne, Dijon, France
VOLUME 14
Magnetohydrodynamics: Waves and Shock Waves in Curved Space-Time by
Andre Lichnerowicz Chaire de Physique Mathematique, College de France, Paris, France
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data Lichnerowicz, Andre, 1915Magnetohydrodynamics : waves and shock waves in curved space-time by Andre Lichnerowicz. p. em. -- 0.......... .. .. .. .. .. . .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. . 19 9
VIII. 1 1. -
The case
1:~
< 0 ................................................................. 202
VIII. 12. -
Conclusions ........................................................................ 210
Annex
=0
• Shock waves and alfven waves.
AI. 1. -
Singular shocks ................................................................. 211
Al.2.-
Compatibility between shock waves andAlfven waves...... ... .......... ...... ........ .. .. ...... .. ...... .. ........ .... .... ........... 220
TABLE OF CONTENTS
ix
Annex II - Magnetosonic rays.
All. 1 . -
Directions of the rays....................................................... 226
All.2.-
Action of 6 on the direction of the ray............................
229
Annex Ill - Classical approximations of. the relativistic shock equations.
Alii. 1.-
The frame connected with the shock ......... ,.......................
232
Alll.2.-
Classical approximation...................................................
232
Bibliography...................................................................................
235
Note - Approach to a quantum theory of fields for a curved space-time.
I •
Tensor propagators............................................................. 237
Nl.l.-
Orientations over a space-time........................................ 237
Nl.2.-
Global hyperbolicity ......................................................... 239
Nl.3.-
Bitensors and Di rae bitensors.......................................... 2 40
Nl.4.-
Linear differential-tensor operators associated with g .. 242
Nl.5.-
Elementary Kernels and propagators...............................
Nl.6.-
Tensor propagators relative to the space-time of
244
Minkowski ......................................................................... 249 Nl.7.-
Propagators relative to the operator (D. + IJ)................. 252
TABLE OF CONTENTS
X
II
- Applications
to
quantization
problems
over
a
curved
space-time.
Nil. 1.-
Commutator for vector Meson .......................................... Commutator for a free electromagnetic field ................... Commutator for a varying gravitational field with mass Commutator for a varying gravitational field without mass term......................................................................... Creation. Annihilation operators ...................................... Dirac field.........................................................................
25
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