Living Reviews in Relativity

"On the History of Unified Field Theories"
by
Hubert F. M. Goenner  

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Abstract
1 Introduction
1.1 Preface
1.2 Introduction to part I
2 The Possibilities of Generalizing General Relativity: A Brief Overview
2.1 Geometry
2.2 Dynamics
2.3 Number field
2.4 Dimension
3 Early Attempts at a Unified Field Theory
3.1 First steps in the development of unified field theories
3.2 Early disagreement about how to explain elementary particles by field theory
4 The Main Ideas for Unification between about 1918 and 1923
4.1 Weyl’s theory
4.2 Kaluza’s five-dimensional unification
4.3 Eddington’s affine theory
5 Differential Geometry’s High Tide
6 The Pursuit of Unified Field Theory by Einstein and His Collaborators
6.1 Affine and mixed geometry
6.2 Further work on (metric-) affine and mixed geometry
6.3 Kaluza’s idea taken up again
6.4 Distant parallelism
7 Geometrization of the Electron Field as an Additional Element of Unified Field Theory
7.1 Unification of Maxwell’s and Dirac’s equations, of electrons and light
7.2 Dirac’s electron with spin, Einstein’s teleparallelism, and Kaluza’s fifth dimension
7.3 Einstein, spinors, and semi-vectors
8 Less Than Unification
9 Mutual Influences Among Mathematicians and Physicists?
10 Public Reception of Unified Field Theory at the Time
11 Conclusion
12 Acknowledgements
Open References References
Footnotes
Biographies