notes

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index

)

The Road to Reality by Roger Penrose in 2004

13. Symmetry groups

14. Calculus on manifolds

15. Fibre bundles and gauge connections

15.1 Some physical motivations for fibre bundles

15.2 The mathematical idea of a bundle

15.3 Cross-sections of bundles

15.4 The Clifford bundle

15.5 Complex vector bundles, (co)tangent bundles

15.6 Projective spaces

15.7 Non-triviality in a bundle connection

15.8 Bundle curvature

16. The ladder of infinity

17. Spacetime

18. Minkowskian geometry

19. The classical fields of Maxwell and Einstein

20. Lagrangians and Hamiltonians

21. The quantum principle

22. Quantum algebra, geometry, and spin

23. The entangled quantum world

24. Dirac’s electron and antiparticles

25. The standard model of particle physics

26. Quantum field theory

27. The big bang and its thermodynamic legacy

28. Speculative theories of the early universe

29. The measurement paradox

30. Gravity’s role in quantum state reduction

31. Supersymmetry, supra-dimensionality, and strings

32. Einstein’s narrower path; loop variables

33. More radical perspectives; twistor theory

34. Where lies the road to reality