Geometrical Methods of Mathematical Physics

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Cambridge University Press, Jan 28, 1980 - Mathematics - 250 pages
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In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
  

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Contents

I
1
III
5
IV
9
V
11
VI
13
VII
16
VIII
20
IX
23
LXXII
130
LXXIII
131
LXXIV
132
LXXV
134
LXXVII
135
LXXVIII
136
LXXIX
137
LXXX
138

XI
26
XII
28
XIII
29
XIV
30
XVI
31
XVII
34
XVIII
35
XIX
37
XX
38
XXI
42
XXII
43
XXIV
47
XXV
49
XXVI
50
XXVII
51
XXVIII
52
XXIX
55
XXX
56
XXXI
57
XXXII
58
XXXIII
59
XXXV
60
XXXVI
63
XXXVII
64
XXXIX
68
XL
70
XLI
71
XLII
73
XLIII
74
XLV
76
XLVI
78
XLVII
79
XLVIII
81
XLIX
83
L
85
LI
86
LII
88
LIII
89
LV
92
LVI
95
LVII
101
LVIII
105
LIX
108
LX
112
LXI
113
LXIII
115
LXIV
117
LXV
119
LXVI
120
LXVIII
121
LXX
125
LXXI
128
LXXXI
140
LXXXII
142
LXXXIII
143
LXXXIV
144
LXXXV
147
LXXXVI
150
LXXXVII
152
LXXXVIII
154
LXXXIX
157
XC
158
XCI
160
XCII
161
XCIII
163
XCIV
164
XCV
165
XCVI
167
XCVII
168
XCVIII
169
XCIX
170
CI
171
CII
174
CIII
175
CIV
179
CV
180
CVI
181
CVIII
182
CIX
183
CX
184
CXI
186
CXII
190
CXIII
192
CXIV
195
CXV
197
CXVI
199
CXVII
201
CXVIII
203
CXIX
205
CXX
207
CXXI
208
CXXII
210
CXXIV
212
CXXV
214
CXXVI
215
CXXVII
216
CXXVIII
218
CXXIX
219
CXXX
222
CXXXI
224
CXXXII
244
CXXXIII
246
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About the author (1980)

Bernard Schutz has done research and teaching in general relativity and especially its applications in astronomy since 1970. He is the author of more than 200 publications, including A First Course in General Relativity and Gravity from the Ground Up (both published by Cambridge University Press). Schutz currently specialises in gravitational wave research, studying the theory of potential sources and designing new methods for analysing the data from current and planned detectors. He is a member of most of the current large-scale gravitational wave projects: GEO600 (of which he is a PI), the LIGO Scientific Collaboration, and LISA. Schutz is a Director of the Max Planck Institute for Gravitational Physics, also known as the Albert Einstein Institute (AEI), in Potsdam, Germany. He holds a part-time chair in Physics and Astronomy at Cardiff University, Wales, as well as honorary professorships at Potsdam and Hanover universities in Germany. Educated in the USA, he taught physics and astronomy for twenty years at Cardiff before moving to Germany in 1995 to the newly-founded AEI. In 1998 he founded the open-access online journal Living Reviews in Relativity. The Living Reviews family now includes six journals. In 2006 he was awarded the Amaldi Gold Medal of the Italian Society for Gravitation (SIGRAV), and in 2011 he received an honorary DSc from the University of Glasgow. He is a Fellow of the American Physical Society and the Institute of Physics, an Honorary Fellow of the Royal Astronomical Society, and a member of the Learned Society of Wales, the German Academy of Natural Sciences Leopoldina and the Royal Society of Arts and Sciences, Uppsala.

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