Mathematical Principles of Theoretical Physics

INDEX 499

dynamic transition theory, 418 , 450
classification, 419

E

E ̈otv ̈os, 63
Eddington coordinate transformation, 434
Eightfold Way, 267
Einstein energymomentum relation, 56
Einstein equation
non-well-posedness of, 193
Einstein equations
non well-posedness, 194
Einstein gravitational field equations, 35 ,
68 , 398 , 400 , 429
Einstein mass-energy formula, 53
Einstein’s theory of general relativity, 60
Einstein-Hilbert action, 67
Einstein-Hilbert functional,67, 68
derivative operator, 147
elastic scatterring, 227
elastic waves, 81
electric charge, 180 , 257
electric field, 54
electromagnetic force, 180 , 215
electromagnetic potential, 50 , 407
electromagnetism, 14 , 181
electron degeneracy pressure, 436
electron structure, 309
electron-positron pair
creation and annihilation, 300
electroweak theory, 244
problems in, 249
elementary particle
strong interaction potential of, 218
elliptic operator
negative eigenvalues of, 169
elliptical galaxy, 442 , 446
energy conservation, 264 , 303
energy level, 358 , 367
energy levels, 166
energy operator, 333
energy rule, 303
energy spectrum, 371
discreteness, 373

energy-momentum conservation,

406,407

energy-momentum tensor, 400

of idealized fluid, 400

energy-momentum vector, 51

equation of state, 406 , 408 , 428

essence of physics, 34

expansion of the Universe, 456

F

fermion, 254

field equations

for the strong interaction, 216

for the weak interaction, 217

field theory

multi-particle system, 377

first Betti number, 141

flatness problem, 463

fluid dynamic equations, 396 , 407

7.1.4 Momentum representation

four forces, 180

four interactions, 180

Fredholm Alternative Theorem, 133

Friedmann cosmology, 459

fundamental representation, 271

G

G-parity, 260

G. Lemaˆıtre, 457

galaxies, 442

galaxy, 412

galaxy cluster, 445

galaxy types, 442

Galilean invariance, 44

gauge invariance, 44 , 70 , 78

gauge symmetry

physical implication of, 188

gauge symmetry breaking, 188

principle of, 189

gauge transformation, 118

SU( 2 ), 187

gauge-fixing problem, 208

non well-posedness of, 209

Gauss formula,131,132