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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).

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Cédric Lorcé

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  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

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