Space, Time, Matter

Cover
Cosimo, Inc., 01.01.2010 - 350 Seiten
In this classic text first published in German in 1918-this is a translation by HENRY L. BROSE (1890-1965) of the 1921 fourth edition-Weyl considers the role of Euclidean space in physics and the mathematics of Einstein's general theory of relativity, exploring: foundations of affine and metrical geometry conception of n-dimensional geometry tensor algebra the stationary electromagnetic field Riemann's geometry affinely connected manifolds space metrics from the point of view of the Theory of Groups relativistic geometry, kinematics, and optics electrodynamics of moving bodies mechanics of the principle of relativity mass and energy gravitational waves concerning the interconnection of the world as a whole and more.HERMANN KLAUS HUGO WEYL (1885-1955)was a German mathematician who spent most of his life working in Zurich, Switzerland. When the Nazi party began to gain power he fled to a job at the Institute of Advanced Study in Princeton, New Jersey where he continued to develop his representation theory. He was one of the most influential mathematicians of the 20th century. He greatly impacted theoretical physics and number theory and was the first to combine general relativity and electromagnetism
 

Inhalt

EUCLIDEAN SPACE ITS MATHEMATICAL FORM AND ITS RÔLE IN PHYSICS 1 Derivation of the Elementary Conceptions of Space from that...
1
Foundations of Affine Geometry
2
Conception of ndimensional Geometry Linear Algebra Quadratic Forms
3
Foundations of Metrical Geometry
4
Tensors
5
Tensor Algebra Examples
6
7 Symmetrical Properties of Tensors
7
Tensor Analysis Stresses
8
RELATIVITY OF SPACE AND TIME 19 Galileis and Newtons Principle of Relativity
149
Electrodynamics of Varying Fields Lorentzs Theorem of Relativity
160
Einsteins Principle of Relativity
169
Relativistic Geometry Kinematics and Optics
179
Electrodynamics of Moving Bodies
188
Mechanics of the Principle of Relativity
196
Mass and Energy
200
Mies Theory
206

The Stationary Electromagnetic Field
9
Note on NonEuclidean Geometry
10
Riemanns Geometry
11
Riemanns Geometry continued Dynamical View of Metrics
12
Tensors and Tensordensities in an Arbitrary Manifold
13
Affinely Connected Manifolds
14
Curvature
15
Metrical Space
16
Remarks on the Special Case of Riemanns Space
17
Space Metrics from the Point of View of the Theory of Groups CHAPTER III
18
11
29
27
46
33
51
43
54
Relativity of Motion Metrical Field and Gravitation
218
Einsteins Fundamental Law of Gravitation
229
Stationary Gravitational Field Relationship with Experience
240
Gravitational Waves
248
Further Rigorous Solutions of the Statical Problem of Gravitation
259
Energy of Gravitation Laws of Conservation
268
World Metrics as the Origin of Electromagnetic Phenomena
282
Application of the Simplest Principle of Action Fundamental
295
BIBLIOGRAPHICAL REFERENCES
319
196
321
INDEX
325
206
328
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