1 / 46

Cédric Lorcé

Cédric Lorcé. The proton spin decomposition : Path dependence and gauge symmetry. IPN Orsay - LPT Orsay. May 7 2013, JLab , Newport News, VA, USA. The decompositions in a nutshell. Jaffe- Manohar (1990). L q. S q. S g. L g. The decompositions in a nutshell. Ji (1997).

ifama
Download Presentation

Cédric Lorcé

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Cédric Lorcé The proton spin decomposition: Pathdependence and gauge symmetry IPN Orsay - LPT Orsay • May 7 2013, JLab, Newport News, VA, USA

  2. The decompositions in a nutshell • Jaffe-Manohar (1990) Lq Sq Sg Lg

  3. The decompositions in a nutshell • Ji (1997) • Jaffe-Manohar (1990) Lq Lq Sq Sq Sg Jg Lg

  4. The decompositions in a nutshell • Ji (1997) • Jaffe-Manohar (1990) Lq Lq Sq Sq Sg Jg Lg • Chen et al. (2008) Lq Sq Sg Lg Gauge-invariant extension (GIE)

  5. The decompositions in a nutshell • Ji (1997) • Jaffe-Manohar (1990) Lq Lq Sq Sq Sg Jg Lg • Chen et al. (2008) • Wakamatsu (2010) Lq Lq Sq Sq Lg Sg Sg Lg Gauge-invariant extension (GIE)

  6. The decompositions in a nutshell Canonical Kinetic • Ji (1997) • Jaffe-Manohar (1990) Lq Lq Sq Sq Sg Jg Lg • Chen et al. (2008) • Wakamatsu (2010) Lq Lq Sq Sq Lg Sg Sg Lg Gauge-invariant extension (GIE)

  7. The Chen et al. approach [Chen et al. (2008,2009)] [Wakamatsu (2010,2011)]

  8. The Chen et al. approach [Chen et al. (2008,2009)] [Wakamatsu (2010,2011)] Gauge transformation

  9. The Chen et al. approach [Chen et al. (2008,2009)] [Wakamatsu (2010,2011)] Gauge transformation Pure-gauge covariant derivatives

  10. The Chen et al. approach [Chen et al. (2008,2009)] [Wakamatsu (2010,2011)] Gauge transformation Pure-gauge covariant derivatives Field strength

  11. The canonicalformalism [C.L. (2013)] Textbook Lagrangian Dynamical variables

  12. The canonicalformalism [C.L. (2013)] Textbook Lagrangian Dynamical variables Gauge covariant

  13. The canonicalformalism [C.L. (2013)] Textbook Lagrangian Dynamical variables Gauge covariant Gauge invariant Dirac variables [Dirac (1955)] [Mandelstam (1962)] Dressing field Gauge transformation

  14. The analogywith General Relativity [C.L. (2012,2013)] Dual role

  15. The analogywith General Relativity [C.L. (2012,2013)] Dual role Pure gauge Physicalpolarizations Degrees of freedom

  16. The analogywith General Relativity [C.L. (2012,2013)] Dual role Pure gauge Physicalpolarizations Degrees of freedom Geometricalinterpretation Parallelism Curvature

  17. The analogywith General Relativity [C.L. (2012,2013)] Dual role Pure gauge Physicalpolarizations Degrees of freedom Geometricalinterpretation Parallelism Curvature Inertial forces Analogywith General Relativity Gravitational forces

  18. The geometricalinterpretation [Hatta (2012)] [C.L. (2012)] Parallel transport

  19. The geometricalinterpretation [Hatta (2012)] [C.L. (2012)] Parallel transport

  20. The geometricalinterpretation [Hatta (2012)] [C.L. (2012)] Parallel transport

  21. The geometricalinterpretation [Hatta (2012)] [C.L. (2012)] Parallel transport Pathdependent! Stueckelbergsymmetry

  22. The gauge symmetry [C.L. (in preparation)] Quantum electrodynamics « Physical » « Background »

  23. The gauge symmetry [C.L. (in preparation)] Quantum electrodynamics « Physical » « Background » Passive

  24. The gauge symmetry [C.L. (in preparation)] Quantum electrodynamics « Physical » « Background » Passive Active

  25. The gauge symmetry [C.L. (in preparation)] Quantum electrodynamics « Physical » « Background » Passive Active Active x (Passive)-1

  26. The gauge symmetry [C.L. (in preparation)] Quantum electrodynamics « Physical » « Background » Stueckelberg Passive Active Active x (Passive)-1

  27. The semanticambiguity Quid ? « physical » « measurable » « gauge invariant »

  28. The semanticambiguity Quid ? « physical » « measurable » « gauge invariant » Observables Measurable, physical, gauge invariant (active and passive) E.g. cross-sections

  29. The semanticambiguity Quid ? « physical » « measurable » « gauge invariant » Observables Measurable, physical, gauge invariant (active and passive) E.g. cross-sections Path Stueckelberg Background Expansion scheme dependent E.g. collinearfactorization

  30. The semanticambiguity Quid ? « physical » « measurable » « gauge invariant » Observables Measurable, physical, gauge invariant (active and passive) E.g. cross-sections Path Stueckelberg Background Expansion scheme dependent E.g. collinearfactorization Quasi-observables « Measurable », « physical », « gauge invariant » (onlypassive) E.g. parton distributions

  31. The local limit Local limit of quasi-observables Pathdependence

  32. The local limit Local limit of quasi-observables Pathdependence Genuinelocal quantitiesare pathindependent ! Parametrized by formfactors

  33. The local limit Local limit of quasi-observables Pathdependence Genuinelocal quantitiesare pathindependent ! Parametrized by formfactors Passive and active Passive and pathindependent Passive and local « True » gauge invariance : [Ji (2009)]

  34. The twist-2 OAM [C.L., Pasquini (2011)] [C.L., Pasquini, Xiong, Yuan (2012)] [Hatta (2012)] Quark Wigner operator

  35. The twist-2 OAM [C.L., Pasquini (2011)] [C.L., Pasquini, Xiong, Yuan (2012)] [Hatta (2012)] Quark Wigner operator Quark OAM operator

  36. The twist-2 OAM [C.L., Pasquini (2011)] [C.L., Pasquini, Xiong, Yuan (2012)] [Hatta (2012)] Quark Wigner operator Quark OAM operator Exact relation « Vorticity »

  37. The pathdependence [Ji, Xiong, Yuan (2012)] [Hatta (2012)] [C.L. (2013)] Canonical quark OAM operator

  38. The pathdependence [Ji, Xiong, Yuan (2012)] [Hatta (2012)] [C.L. (2013)] Canonical quark OAM operator x-basedFock-Schwinger Coincideslocallywithkinetic quark OAM

  39. The pathdependence [Ji, Xiong, Yuan (2012)] [Hatta (2012)] [C.L. (2013)] Canonical quark OAM operator x-basedFock-Schwinger Light-front ISI FSI Drell-Yan SIDIS Coincideslocallywithkinetic quark OAM Naive T-even

  40. The summary Canonical Kinetic • Not observable • Ji (1997) • Observable • Jaffe-Manohar (1990) Lq Lq Sq Sq Sg Jg Lg • Chen et al. (2008) • Quasi-observable • Wakamatsu (2010) • Quasi-observable Lq Lq Sq Sq Lg Sg Sg Lg

  41. Backup slides

  42. The parton distributions GTMDs • [PRD84 (2011) 014015] • [PRD85 (2012) 114006] TMDs TMFFs GPDs • [PRD84 (2011) 034039] • [PLB710 (2012) 486] • [JHEP1105 (2011) 041] TMCs PDFs FFs • [PRD79 (2009) 014507] • [Nucl. Phys. A825 (2009) 115] • [PRL104 (2010) 112001] • [PRD79 (2009) 113011] Charges • [PRD74 (2006) 054019] • [PRD78 (2008) 034001] • [PRD79 (2009) 074027] • Phase-spacedensities

  43. The spin-spin-orbitcorrelations [C.L., Pasquini (2011)]

  44. The light-frontwavefunctions Overlaprepresentation Momentum Polarization Light-front quark models Wigner rotation • [PRD74 (2006) 054019] • [PRD78 (2008) 034001] • [PRD79 (2009) 074027]

  45. The orbital angularmomentum OAM Kinetic GPDs Canonical (naive) TMDs Canonical GTMDs Phenomenologicalcomparison but

  46. The gauge-invariant extension (GIE) Gauge-variant operator GIE2 GIE1 Gauge « Natural » gauges Rest Center-of-mass Infinitemomentum Lorentz-invariant extensions ~ « Natural » frames

More Related