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Dipolar Quantization of Conformal Field Theories Tsukasa Tada iTHES RIKEN Nishina Center & iTHES Interdisciplinary Theoretical Science Research Group Sine Square Deformation Recent works include Wen, Ryu, Ludwig, PRB 93 (2016)235119

  1. Dipolar Quantization of Conformal Field Theories Tsukasa Tada iTHES RIKEN Nishina Center & iTHES Interdisciplinary Theoretical Science Research Group

  2. Sine Square Deformation Recent works include Wen, Ryu, Ludwig, PRB 93 (2016)235119 Okunishi, PTEP(2016)063A02

  3. Sine Square Deformation Recent works include Wen, Ryu, Ludwig, PRB 93 (2016)235119 Okunishi, PTEP(2016)063A02 SSD ground state for CFT H. Katsura (’12)

  4. Sine Square Deformation is the deformation of CFT ada, JPA 48 (2015)315402 Ishibashi, T Ishibashi, T ada, arXiv:1602.01190 continuous Virasoro algebra altered Hilbert space

  5. Sine Square Deformation is the deformation of CFT ada, JPA 48 (2015)315402 Ishibashi, T Ishibashi, T ada, arXiv:1602.01190 Dipolar Quantization

  6. Dipolar Quantization Radial Quantization

  7. Radial Quantization

  8. Dipolar Quantization

  9. Dipolar Quantization is another time foliation Hamiltonian c.f. Kiermaier, Sen, Zwiebach (’08)

  10. Dipolar Quantization is another time foliation Hamiltonian Energy states? c.f. Kiermaier, Sen, Zwiebach (’08)

  11. Dipolar Quantization is another time foliation conserved charges

  12. Dipolar Quantization is another time foliation conserved charges

  13. Dipolar Quantization is another time foliation conserved charges

  14. Dipolar Quantization is another time foliation conserved charges

  15. Dipolar Quantization Define c.f.

  16. Dipolar Quantization Define c.f.

  17. Dipolar Quantization

  18. Dipolar Quantization Continuous eigenvalues for Infinite circumference

  19. Dipolar Quantization is another time foliation Hermitian conjugate

  20. ���������� ����������� Radial Dipolar Quantization Quantization

  21. Overview Quantum Spacetime system finite Radial Symmetry Quantization space Di fg erent Hilbert Space infinite Dipolar space Quantization

  22. Why Dipolar ? Generators for conformal symmetry “Time” translation [translation] for radial quantization [dilation] [SCT] [rotation]

  23. Why Dipolar ? [translation] [dilation] [SCT]

  24. Why Dipolar ? Massive Rep. Massless Rep. (discrete) (continuous) Radial Dipolar Quantization Quantization

  25. Why Dipolar ? Radial Dipolar Quantization Quantization

  26. Why Dipolar ? Radial Dipolar Quantization Quantization

  27. Why Dipolar ?

  28. Why Dipolar ? Dipolar Quantization

  29. Why Dipolar ? Gap or “Mass” Dipolar Quantization

  30. Minkowskian CFT

  31. Minkowskian CFT SCT

  32. Minkowskian CFT

  33. Minkowskian CFT

  34. Minkowskian CFT

  35. Minkowskian CFT

  36. Minkowskian CFT

  37. Minkowskian CFT

  38. Minkowskian CFT

  39. Minkowskian CFT

  40. Minkowskian CFT

  41. Summary Dipolar quantization for CFT Sine-square deformation Continuous Virasoro algebra Infinite circumference Also works for Minkowskian

  43. Conformal Quantum Mechanics de Alfaro, Fubini, Furlan (’76)

  44. Conformal Quantum Mechanics de Alfaro, Fubini, Furlan (’76) Claus, Derix, Kallosh, Kumar, T ownsend, Van Proeyen (’98) Michelson, Strominger (’99)

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