Snygg J. — Clifford algebra: a computational tool for physicists :: Электронная библиотека попечительского совета мехмата МГУ

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Snygg J. — Clifford algebra: a computational tool for physicists

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Название: Clifford algebra: a computational tool for physicists

Автор: Snygg J.

Аннотация:

Clifford algebras have become an indispensable tool for physicists at the cutting edge of theoretical investigations. Applications in physics range from special relativity and the rotating top at one end of the spectrum, to general relativity and Dirac's equation for the electron at the other. Clifford algebras have also become a virtual necessity in some areas of physics, and their usefulness is expanding in other areas, such as algebraic manipulations involving Dirac matrices in quantum thermodynamics; Kaluza- Klein theories and dimensional renormalization theories; and the formation of superstring theories. This book, aimed at beginning graduate students in physics and math, introduces readers to the techniques of Clifford algebras.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 352

Добавлена в каталог: 26.08.2014

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Предметный указатель

Reverse of a Clifford number, real      57—58 307
Ricci rotation coefficients      92
Ricci tensor      99
Richards, James A, Jr.      38
Riefin, Edgar      11
Riemann curvature tensor, definition      78—79 96—97
Riemann curvature tensor, formula for in terms of Christoffel symbols      80
Riemann curvature tensor, symmetries of      96—100
Riesz, Marcel      57 76 288
Riesz, Marcel, theorem on universal Clifford algebras      43 288—290
Rindler, Wolfgang      xiv 89 97 322
Rotation as product of reflections in $E^{n}$       9
Rotation as product of two reflections in $E^{3}$       5—8
Sauter, Fritz      170
scalar      8—9
Scalar product for two p-forms      57—58
Scalar product for two real Clifford numbers      57—58
Scalar product for two real vectors      47
Scalar product, complex      171
Schiffer, Menachem      217
Schroedinger's equation, solutions of, from limits of solutions for Dirac's equation      214—215
Schwarzschild metric      111—128 264—266
Schwarzschild metric, Eddington's form of      283 286
Schwarzschild radius      116
Schwarzschild, Karl      111
Semicolon notation      89
Shapiro, Arnold      294
Signature matrix $n_{jk}$       43
Simple Clifford number      309
Simple unit space-space bivector      309
Simple unit space-time bivector      309—310
Singular Clifford algebra      76
Singular metric      76 79
Sirlin, Alberto      170
Sobczyk, Garret      57
Sommerfeld, Arnold      170
Soni, Raj Pal      209 214—215
Special relativity      25—40
Spherical coordinates      45 52—53
Spherical excess of a spherical triangle      62

Spherical harmonic Clifford functions      189—203
Spherical harmonics      191
Spherical triangle, area of      61
Spin angle for spinning top      14
Stegun, Irene A.      191
Stehney, Ann      267
Step up and step down operators      192
Stephani, H.      264
Stoke's theorem, generalized      161—169
SU(2) group      11
Tangent space      46
Tangent vector      46
Tensor product      295
Tensor, components of      51
Thirring, Hans      246
Thorne, Kip      116
Tilt angle for spinning top      14
Torsion-free differential operator      86
Total quantum number for Schroedinger's equation      212 215
Universal Clifford algebras      44 288—290
Upper index Dirac matrices      48
Vector, 1-vector      42
Vector, isotropic      76
Vector, light-like      76
Vector, null      76
Vector, p-vector      42
Vector, position      45
Vector, potential      140
Vierbem      94
Vulcan, hypothetical planet      127
Wald, Robert M.      89 116 150
Wedderburn, Joseph H.M.      308
Wedderburn, Joseph H.M., theorem of      308
Wehr, Russell M.      38
Weyl matrix      251—253
Weyl tensor      250—251
Wheeler, John Archibald      116
World velocity      36
Yang — Mills fields      xv 144—154
Zuber, Jean-Bernard      179

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