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Frankel T. — The geometry of physics: an introduction
Frankel T. — The geometry of physics: an introduction



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Название: The geometry of physics: an introduction

Автор: Frankel T.

Аннотация:

This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism, thermodynamics, the deformation tensors of elasticity, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should also be of interest to mathematics students. This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics. It can be used as a course text or for self study.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 688

Добавлена в каталог: 15.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Space-time notation      141
Spacelike      193
Spatial metric      298
Spatial slice      316
Special      392
Special, linear group, Sl(n)      11 392
Special, orthogonal group SO(n)      392
Special, unitary group SU(n)      392
Sphere lifting theorem      605
Spin structure      515—518
Spinor, "representation" of SO(3)      497
Spinor, "representation" of the Lorentz group      509
Spinor, 2-component      497
Spinor, 2-component, left- and right-handed      513
Spinor, adjoint      532
Spinor, bundle $\mathfrak{S} M$      517
Spinor, connection      518—521
Spinor, cospinor      513
Spinor, Dirac or 4-component      513
Spinor, group Spin(3)      497
Stability      324
Stability, 2-component, subgroup      457
Stiefel manifold      459 616
Stiefel vector field      426
Stokes's theorem      111—114
Stokes's theorem for pseudoforms      117
Stokes's theorem, generalized      155
Stored energy of deformation      623—626
Stress forms, Cauchy      618
Stress forms, Cauchy, symmetry      620
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(N)      392 493—497
Subalgebra      411
Subgroup      411
Subgroup, isotropy = little = stability      457
Submanifold      26
Submanifold of $M^{n}$      29
Submanifold of $\mathbb{R}^{n}$      4 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      51
Tangent space      7 25
Tangent vector      23
Tellegen's theorem      646
Tensor, analysis      298—303
Tensor, Cauchy — Green      82
Tensor, contravariant      59
Tensor, covariant      58
Tensor, deformation      82 625
Tensor, metric      58
Tensor, mixed      60
Tensor, mixed, linear transformation      61
Tensor, product      59 66
Tensor, product, representation      482
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      249
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 area      221 322
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 as differential operator      25
Vector, analysis      92 136—138
Vector, bundle      413—419
Vector, bundle-valued form      488
Vector, contravariant or tangent      23
Vector, coordinate      25
Vector, covariant = covector = 1-form      41
Vector, field      25
Vector, field, along a submanifold      269
Vector, field, flow (1-parameter group) generated by      32 33
Vector, field, integral curve of      31
1 2 3 4
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