Cédric Lorcé IPN Orsay - LPT Orsay May 7 2013, JLab, Newport News, VA, USA The proton spin decomposition: Path dependence and gauge symmetry
Cédric Lorcé
Feb 22, 2016
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). - PowerPoint PPT Presentation
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Cédric LorcéIPN Orsay - LPT Orsay
May 7 2013, JLab, Newport News, VA, USA
The proton spin decomposition:Path dependence and gauge
symmetry
Jaffe-Manohar (1990)
The decompositions in a nutshell
Sq
SgLg
Lq
Ji (1997)Jaffe-Manohar (1990)
The decompositions in a nutshell
Sq
SgLg
Lq Sq
Jg
Lq
Ji (1997)Jaffe-Manohar (1990)
Chen et al. (2008)
The decompositions in a nutshell
Sq
SgLg
Lq
Sq
SgLg
Lq
Sq
Jg
Lq
Gauge-invariant extension (GIE)
Wakamatsu (2010)
Ji (1997)Jaffe-Manohar (1990)
Chen et al. (2008)
The decompositions in a nutshell
Sq
SgLg
Lq
Sq
SgLg
Lq Sq
SgLg
Lq
Sq
Jg
Lq
Gauge-invariant extension (GIE)
Wakamatsu (2010)
Ji (1997)Jaffe-Manohar (1990)
Chen et al. (2008)
Canonical Kinetic
The decompositions in a nutshell
Sq
SgLg
Lq
Sq
SgLg
Lq Sq
SgLg
Lq
Sq
Jg
Lq
Gauge-invariant extension (GIE)
The Chen et al. approach[Chen et al. (2008,2009)] [Wakamatsu (2010,2011)]
The Chen et al. approach
Gauge transformation
[Chen et al. (2008,2009)] [Wakamatsu (2010,2011)]
The Chen et al. approach
Gauge transformation
Pure-gauge covariant derivatives
[Chen et al. (2008,2009)] [Wakamatsu (2010,2011)]
The Chen et al. approach
Gauge transformation
Field strength
Pure-gauge covariant derivatives
[Chen et al. (2008,2009)] [Wakamatsu (2010,2011)]
The canonical formalism
Textbook
Dynamical variables
Lagrangian
[C.L. (2013)]
The canonical formalism
Textbook
Gauge covariant
Dynamical variables
Lagrangian
[C.L. (2013)]
The canonical formalism
Textbook
Gauge covariant
Gauge invariant
Dynamical variables
Lagrangian
Dirac variables
Dressing field Gauge transformation
[Dirac (1955)][Mandelstam
(1962)]
[C.L. (2013)]
The analogy with General Relativity[C.L. (2012,2013)]
Dual role
Pure gauge
Physical polarizations
The analogy with General Relativity
Degrees of freedom
[C.L. (2012,2013)]
Dual role
Pure gauge
Physical polarizations
The analogy with General Relativity
Geometrical interpretationParallelism Curvature
Degrees of freedom
[C.L. (2012,2013)]
Dual role
Pure gauge
Physical polarizations
Analogy with General
Relativity
The analogy with General Relativity
Geometrical interpretationParallelism Curvature
Inertial forces
Gravitational forces
Degrees of freedom
[C.L. (2012,2013)]
Dual role
The geometrical interpretation[Hatta (2012)]
[C.L. (2012)]Parallel transport
The geometrical interpretation[Hatta (2012)]
[C.L. (2012)]Parallel transport
The geometrical interpretation[Hatta (2012)]
[C.L. (2012)]Parallel transport
The geometrical interpretation[Hatta (2012)]
[C.L. (2012)]Parallel transport
Path dependent!
Stueckelberg symmetry
The gauge symmetry
Quantum electrodynamics« Physical »
[C.L. (in preparation)]
« Background »
The gauge symmetry
Quantum electrodynamics
Passive
« Physical »
[C.L. (in preparation)]
« Background »
The gauge symmetry
Quantum electrodynamics
Passive Active
« Physical »
[C.L. (in preparation)]
« Background »
The gauge symmetry
Quantum electrodynamics
Passive Active
« Physical »
[C.L. (in preparation)]
« Background »
Active x (Passive)-1
The gauge symmetry
Quantum electrodynamics
Passive Active
« Physical »
[C.L. (in preparation)]
« Background »
Active x (Passive)-1
Stueckelberg
The semantic ambiguity
« measurable »Quid ? « physical »
« gauge invariant »
The semantic ambiguity
Observables
« measurable »Quid ? « physical »
« gauge invariant »
Measurable, physical, gauge invariant (active and passive)E.g. cross-sections
The semantic ambiguity
PathStueckelbergBackground
Observables
« measurable »Quid ? « physical »
« gauge invariant »
Measurable, physical, gauge invariant (active and passive)
Expansion scheme
E.g. cross-sections
dependentE.g. collinear factorization
The semantic ambiguity
PathStueckelbergBackground
Observables
Quasi-observables
« measurable »Quid ? « physical »
« gauge invariant »
Measurable, physical, gauge invariant (active and passive)
« Measurable », « physical », « gauge invariant » (only passive)
Expansion scheme
E.g. cross-sections
E.g. parton distributions
dependentE.g. collinear factorization
The local limit
Local limit of quasi-observables
Path dependence
The local limit
Local limit of quasi-observables
Path dependence
Genuine local quantities are path independent !
Parametrized by form factors
The local limit
Local limit of quasi-observables
Path dependence
Genuine local quantities are path independent !
Parametrized by form factors
« True » gauge invariance :Passive and activePassive and path independentPassive and local
[Ji (2009)]
The twist-2 OAM
Quark Wigner operator
[C.L., Pasquini (2011)][C.L., Pasquini, Xiong, Yuan (2012)]
[Hatta (2012)]
The twist-2 OAM
Quark Wigner operator
[C.L., Pasquini (2011)][C.L., Pasquini, Xiong, Yuan (2012)]
[Hatta (2012)]
Quark OAM operator
« Vorticity »
The twist-2 OAM
Quark Wigner operator
[C.L., Pasquini (2011)][C.L., Pasquini, Xiong, Yuan (2012)]
[Hatta (2012)]
Quark OAM operator
Exact relation
The path dependence[Ji, Xiong, Yuan (2012)]
[Hatta (2012)][C.L. (2013)]Canonical quark OAM operator
The path dependence[Ji, Xiong, Yuan (2012)]
[Hatta (2012)][C.L. (2013)]
Coincides locally with kinetic quark OAM
Canonical quark OAM operator
x-based Fock-Schwinger
FSIISI
SIDISDrell-Yan
The path dependence[Ji, Xiong, Yuan (2012)]
[Hatta (2012)][C.L. (2013)]
Coincides locally with kinetic quark OAM
Naive T-even
Canonical quark OAM operator
x-based Fock-Schwinger Light-front
Wakamatsu (2010)
Ji (1997)Jaffe-Manohar (1990)
Chen et al. (2008)
Canonical Kinetic
The summary
Sq
SgLg
Lq
Sq
SgLg
Lq Sq
SgLg
Lq
Sq
Jg
Lq
Not observable Observable
Quasi-observableQuasi-observable
Backup slides
[PRD79 (2009) 014507] [Nucl. Phys. A825 (2009) 115]
[PRL104 (2010) 112001][PRD79 (2009) 113011]
GTMDs
TMDs
Charges
PDFs
GPDs
FFsTMCs
TMFFs[PRD84 (2011) 034039]
[PLB710 (2012) 486]
[PRD84 (2011) 014015][PRD85 (2012) 114006]
[JHEP1105 (2011) 041]
[PRD74 (2006) 054019][PRD78 (2008) 034001]
[PRD79 (2009) 074027]
Phase-space densities
The parton distributions
The spin-spin-orbit correlations[C.L., Pasquini (2011)]
Overlap representation
Momentum Polarization
[PRD74 (2006) 054019][PRD78 (2008) 034001][PRD79 (2009) 074027]
Light-front quark models Wigner rotation
The light-front wave functions
OAM
Canonical (naive)
Kinetic
Canonical GTMDs
TMDs
GPDs
Phenomenological comparison
but
The orbital angular momentum
Gauge
GIE1
GIE2
Gauge-variant operator
« Natural » gauges
Lorentz-invariant extensions~
RestCenter-of-mass
Infinite momentum
« Natural » frames
The gauge-invariant extension (GIE)
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