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Gravity and Defects

Gravity and Defects. BERLIN ICRANet Pescara. Hagen Kleinert, FU BERLIN & ICRANet Pescara. Imagine : Single- Valued World . Multivalued World. Warm-up: Ginzburg-Landau Theory. set. FALSE!. Chain Rule :. But this is Ising – like !. Jumps!.

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Gravity and Defects

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  1. Gravity andDefects BERLIN ICRANet Pescara Hagen Kleinert, FU BERLIN & ICRANet Pescara

  2. Imagine: Single-Valued World Multivalued World

  3. Warm-up: Ginzburg-Landau Theory • set FALSE! Chain Rule: But thisisIsing –like!

  4. Jumps! Correct Chain Rule: In 1D, canberemovedbygoingtocoveringgroup U(1) In >1D impossible

  5. Vortex Gauge Field Invariant Field Strength: Axial Gauge

  6. Simplest MULTIVALUED FIELD in 2D Solve:

  7. NOTE: Mother ofTwoImportant Green Functions

  8. Correct Treatment:Ginzburg-Landau Theory • set Chain Rule: XY–like!

  9. ApplicationofMultivaluedFields toMagnetostatics Recall Thomson and Maxwell: W. Thomson (1824-1907) J.C.Maxwell (1831-1879)

  10. GenerateMagnetic FieldbyMultivalued Gauge Transformations ThinFlux Tube:

  11. Also: Magnetic Monopoles Paul Dirac (1902-1984)

  12. Derive: Minimal CouplingFrom Non-holonomicGauge Transformations J.L.Lagrange (1736-1819) Thenactionchangesbysurfacetermsonly: Fornonholonomic Nontrivial

  13. SchrödingerTheory E.Schrödinger (1887-1961) Momentum Solved by Use nonholonomic then with nonzero magnetic field

  14. Multivalued Description ofMagnetism Magnetic Field

  15. Action Gauge Invariance

  16. Integration byparts Integration of Omega Enforcedas Bianchi Identity: Double Gauge Theory: DefectCurrentConserv.:

  17. Recall: Action arises also from GL Theoryof superfluid He In London (hydrodynamic) Limit Thus same formalismholdsfor superfluid He!

  18. GC Sum Over LinescanbetransformedintoDisorder QFT Result: Ginzburg-Landau Theoryof Superfluid Helium

  19. Double-Gauge QFT of Monopoles

  20. Double-Gauge QFT of Monopoles

  21. Now : NontrivialGeometry fromNonholonomicCoordinateTransformations Burgers vectorb

  22. DISCLINATIONS  Frank Vector

  23. FUNDAMENTALS:Universalityof FREE PARTICLE motion:

  24. Nonholonomicimageof isAutoparallel E.Schrödinger (1887-1961) InsteadofGeodesic A.Einstein (1879-1955)

  25. QUANTUM THEORY:Trajectoryisfatfluctuationsausage! Tidalforces on wave packet ?

  26. LatticeDefectTheoryvsAbelian QED on Lattice Latticeformulation Define

  27. CURIOSITY: InducedGravity in `World Crystal´ Elastic Gauge Tfs: Canonical Form MomentumConservation Enforcedas Bianchi Idty: Double Gauge Theory

  28. Dual Representation

  29. BUT NEED

  30. Modify Elastic Action to andfurtherto FLOPPY CRYSTAL

  31. Ifyouwanttoknowmore, readmynewbook Only 38 Euro

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