Frankel T. — The geometry of physics: An introduction :: Электронная библиотека попечительского совета мехмата МГУ

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Frankel T. — The geometry of physics: An introduction

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Название: The geometry of physics: An introduction

Автор: Frankel T.

Аннотация:

Theodore Frankel explains those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms essential to a better understanding of classical and modern physics and engineering. Key highlights of his new edition are the inclusion of three new appendices that cover symmetries, quarks, and meson masses; representations and hyperelastic bodies; and orbits and Morse-Bott Theory in compact lie groups. Geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd

Год издания: 2004

Количество страниц: 717

Добавлена в каталог: 21.02.2015

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Предметный указатель

Stokes's theorem for pseudoforms      117
Stokes's theorem, generalized      155
Stored energy of deformation      623—626
Strain energy      660
Stress forms, Cauchy      618 Stress forms Cauchy symmetry
Stress forms, first Piola — Kirchhoff      622
Stress forms, second Piola — Kirchhoff      623
Stress tensor      295 617
Stress-energy-momentum tensor $T_{ij}$       295
Structure constants      402
Structure constants in a bi-invariant metric      566
Structure group of a bundle      433 452
Structure group of a bundle, reduction      433
SU(2) * U(1)      657
SU(N)      392 493—497
Subalgebra      411
Subgroup      411
Subgroup, isotropy = little = stability      457
Submanifold      26
Submanifold of $M^{n}$       29
Submanifold of $\mathbb{R}^{n}$       8
Submanifold with transverse orientation      115
Submanifold, 1- and 2-sided      84
Submanifold, embedded      27
Submanifold, framed      115
Submanifold, immersed      169
Submersion      181
Summation convention      59
Support      107
Symmetries      527—531
Symplectic form      146
Symplectic manifold      146
Synge's formula      325
Synge's theorem      329
Tangent bundle      48 Tangent bundle unit
Tangent space      7 25
Tangent vector      23
Tellegen's theorem      646
Tensor analysis      298—303
Tensor deformation      82 625
Tensor product      59 66 Tensor representation
Tensor, Cauchy — Green      82
Tensor, contravariant      59
Tensor, covariant      58
Tensor, metric      58
Tensor, mixed      60 Tensor mixed linear
Tensor, rate of deformation      632
Tensor, transformation law      62
Tensor, two-point      622
Theorema egregium      231
Thermodynamics, first law      180
Thermodynamics, second law according to Caratheodory      181
Thermodynamics, second law according to Lord Kelvin      181
Thom's theorem      349
Timelike      193
Topological invariants      346
Topological quantization      468
Topological space      12
Topological space, compact      13
topology      12
Topology, induced or subspace      12
Torsion of a connection      245 Torsion of a connection 2-form
Torsion of a space curve      196
Torus      16
Torus, maximal      393
Transformation group      456
Transition matrix $c_{UV}$       24 254 414
Transition matrix $c_{UV}$ for dual bundles      417
Transition matrix $c_{UV}$ for tangent bundle      417

Transition matrix $c_{UV}$ for tensor product bundle      417
Transition matrix $c_{UV}$ for the cotangent bundle      417
Transitive      456
Translation (left and right)      393
Transversal to a submanifold      34
Transverse orientation      115
Triangulation      346
Tunneling      558
Twisted product      415
Unitary group U(n)      392
Universe, static      292
Universe, stationary      291
Vacuum state      557 558
Vacuum state, tunneling      558
Variation of a map      153
Variation of action      154
Variation of Ricci tensor      306
Variation, external      523
Variation, first, of arc length      232 Variation first of
Variation, internal      523
Variation, second, of arc length      324—332
Variational derivative $\delta$       307 526
Variational equation      128
Variational principles of mechanics      275—281
Variational vector      128 153 272
Vector analysis      92 136—138
Vector as differential operator      25
Vector bundle      413—419 Vector bundle-valued form
Vector covariant = covector = 1-form      41
Vector field      25 Vector field flow
Vector product      92 94 103
Vector, contravariant or tangent      23
Vector, coordinate      25
Vector, gradient      45
Vector, integral      144 308
Vector, invariant      395
Vector, Killing      528
Vector, transformation law      34
Vector, variational      128 153 272
Vector, velocity 4-vector      193
Vector-valued form      248
Velocity field      31
Virtual displacement      276
Voltage as a cochain      644
Volume bundle      488
Volume form      86 88
Volume invariant, in mechanics      148 Volume invariant on
Vorticity      145
Wedge product      see "Exterior product"
Weight diagram      655
Weingarten equations      204
Weizenboeck formulas      370
Weyl's equation for neutrinos      515
Weyl's method of orthogonal projection      647
Weyl's principle of gauge invariance      441
Weyl's theorem on the fundamental group of a Lie group      565 581
Whitney embedding theorem      23
Winding number of a curve      212
Winding number of a Yang — Mills instanton      560 Winding number of a Yang — Mills instanton in terms of field strength
Winding number of a Yang — Mills vacuum      560
Work 1-form in thermodynamics      179
World line      193
Wormhole      446
Yang — Mills action      544
Yang — Mills analogy with electromagnetism      547 548 550
Yang — Mills equations      545
Yang — Mills field strength      539
Yang — Mills instanton      550 Yang — Mills instanton winding
Yukawa — Kemmer      658
zero modes      465

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