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공간과 시간과 물질에 관한 물리와 수학 책.The Book of Space-- Time-- Matter, by Hermann Weyl


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공간과 시간과 물질에 관한 물리와 수학 책.The Book of Space-- Time-- Matter, by Hermann Weyl

Hermann Weyl 저 | 뉴가출판사

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2020-09-08
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공간과 시간과 물질에 관한 물리와 수학 책.The Book of Space-- Time-- Matter, by Hermann Weyl
유클리드의 기하학과 갈릴레오의 천문학 그리고 아이슈타인의 상대성이론 까지의 그리고 물론, 뉴톤의 물리와 수학도 포함되고, 공간및 시간및 물질에 대한 물리적 개념과 수학적 공식을 도입해서 정리한책. 독일로된 책을 영어로 번역한책.
The Book of Space--
Time--Matter,
by Hermann Weyl
Title: Space--Time--Matter
Author: Hermann Weyl
Translator: Henry L. Brose
Language: English
SPACE―TIME―MATTER
BY
HERMANN WEYL
TRANSLATED FROM THE GERMAN BY
HENRY L. BROSE
WITH FIFTEEN DIAGRAMS
METHUEN & CO. LTD.
36 ESSEX STREET W.C.
LONDON

목차

CONTENTS
PAGE
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
CHAPTER I
Euclidean Space. Its Mathematical Formulation and its
Role in Physics
§ 1. Deduction of the Elementary Conceptions of Space from that
of Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
§ 2. The Foundations of Affine Geometry . . . . . . . . . . . . . . . . . . . . . . . 23
§ 3. The Conception of n-dimensional Geometry. Linear Algebra.
Quadratic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
§ 4. The Foundations of Metrical Geometry . . . . . . . . . . . . . . . . . . . . 39
§ 5. Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
§ 6. Tensor Algebra. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
§ 7. Symmetrical Properties of Tensors . . . . . . . . . . . . . . . . . . . . . . . . . 79
§ 8. Tensor Analysis. Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
§ 9. Stationary Electromagnetic Fields. . . . . . . . . . . . . . . . . . . . . . . . . . 94
CHAPTER II
The Metrical Continuum
PAGE
§ 10. Note on Non-Euclidean Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . 113
§ 11. The Geometry of Riemann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
§ 12. Continuation. Dynamical View of Metrical Properties . . . . . . 140
§ 13. Tensors and Tensor-densities in any Arbitrary Manifold . . . . 151
§ 14. Affinely Related Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
§ 15. Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
§ 16. Metrical Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
§ 17. Observations about Riemann’s Geometry as a Special Case. 191
§ 18. Metrical Space from the Point of View of the Theory of
Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
CHAPTER III
Relativity of Space and Time
§ 19. Galilei’s Principle of Relativity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
§ 20. The Electrodynamics of Moving Fields Lorentz’s Theorem of
Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
§ 21. Einstein’s Principle of Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
§ 22. Relativistic Geometry, Kinematics, and Optics . . . . . . . . . . . . . 267
§ 23. The Electrodynamics of Moving Bodies . . . . . . . . . . . . . . . . . . . . 281
§ 24. Mechanics according to the Principle of Relativity. . . . . . . . . . 293
§ 25. Mass and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
§ 26. Mie’s Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
CHAPTER IV
The General Theory of Relativity
PAGE
§ 27. The Relativity of Motion, Metrical Fields, Gravitation . . . . . 325
§ 28. Einstein’s Fundamental Law of Gravitation . . . . . . . . . . . . . . . . 342
§ 29. The Stationary Gravitational Field?Comparison with Ex periment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
§ 30. Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
§ 31. Rigorous Solution of the Problem of One Body. . . . . . . . . . . . . 377
§ 32. Additional Rigorous Solutions of the Statical Problem of
Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
§ 33. Gravitational Energy. The Theorems of Conservation . . . . . . 402
§ 34. Concerning the Inter-connection of the World as a Whole . . 409
§ 35. The Metrical Structure of the World as the Origin of Elec tromagnetic Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
§ 36. Application of the Simplest Principle of Action. The Funda mental Equations of Mechanics . . . . . . . . . . . . . . . . . . . . . . . . 442
Appendix I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
Appendix II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
Bibliographical References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

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