Boost invariant formula/on of the chiral kine/c theory
Shi Pu
The University of Tokyo
Workshop of Recent Developments in QCD and Quantum Field Theories, Nov. 9-12, 2017, Taipei
In coopera/on with Kenji Fukushima ,
Shu Ebihara, Phys.Rev. D96 (2017), 016016
• Introduction to Chiral kinetic theory (CKT)
• CKT with Bjorken expansion
• Summary
Outline
Introduc/on to Chiral kine/c theory
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Chirality and massless fermions
u R
spin
momentum
u L
spin
momentum
Chiral Magnetic Effect (I)
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
u R
spin
momentum
• Magnetic fields
• Nonzero axial chemical potential
• Number of Left handed fermions
≠ Number of Right handed fermions
• Charge current
Ref: Kharzeev, Fukushima, Warrigna, (08,09), etc. ... Cf. Dmitri’s Talk
B
Chiral Magnetic Effect (II)
• Heavy ion collisions: charge separation
Chiral Magnetic Effect (II)
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
• Heavy ion collisions: charge separation
• Weyl Semi-metal: new transport effects
ZrTe
5: arXiv:1412.6543, Nature Physics (2016) doi:10.1038/nphys3648
Chiral Magnetic Effect (II)
• Heavy ion collisions: charge separation
• Weyl Semi-metal: new transport effects
• To the real world: New type of “superconductor”?
“Dissipa/onless transmiXng and processing informa/on
and energy”, Q. Li (BNL), Chiral Ma]er 2016, RIKEN
Kinetic theory
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
• “distribution function” f(x,p,t)
• Ordinary kinetic theory: Boltzmann equation
• Spin effects, massless particles
SP, J.H. Gao, Q. Wang, PRD 83 (2011) 094017
• Hamiltonian formulism, effective theory
Son, Yamamoto, PRL, (2012); PRD (2013)
• Path integration
Stephanov, Yin, PRL (2012);
Chen, Son, Stephanov, Yee, Yin, PRL, (2014);
J.W. Chen, J.Y. Pang, SP, Q. Wang, PRD (2014)
• Wigner function
– hydrodynamics, equilibrium
J.W. Chen, SP, Q. Wang, X.N. Wang, PRL (2013);
– out-of-equilibrium, quantum field theory
Y. Hidaka, SP, D.L. Yang, PRD(RC) (2017) Cf. Di-Lun’s Talk
Chiral kinetic equation (I)
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Ordinary Boltzmann equation
• Particle’s velocity:
• Lorentz force:
• Collision effects:
C[f]
Chiral kinetic equation
• Particle’s velocity:
• External force:
• Berry curvature
• 3D ac/on with Berry phase
Chen, Son, Stephanov, Yee, Yin, PRL, (2014) – Infinitesimal Lorentz Transform
• Global angular momentum conserva/on Chen, Son, Stephanov, PRL, (2015)
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Lorentz symmetry and side-jump (I)
Side-jump (I)
spin
momentum
Orbital angular momentum and spin are conserved separately.
Chen, Son, Stephanov, Yee, Yin, PRL, (2014)
spin
momentum
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Side-jump (II)
spin momentum Orbital angular momentum ?
Spin is NOT conserved!
Chen, Son, Stephanov, Yee, Yin, PRL, (2014)
Side-jump (III)
spin momentum
x has a shift!!!
Chen, Son, Stephanov, Yee, Yin, PRL, (2014)
• Field theory
• Lorentz transforma/on,
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Infinitesimal Lorentz
Transform
Chen, Son, Stephanov, PRL, (2015);
Y. Hidaka, SP, D.L. Yang, (2016) Cf. Di-Lun’s talk
Lorentz symmetry and side-jump (II)
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Chiral kine/c theory + Bjorken expansion
In coopera/on with Kenji Fukushima,
Shu Ebihara, Phys.Rev. D96 (2017), 016016
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Topological charges classical sta/s/cal simula/on
?
Chiral
Magneto-hydrodynamics Chiral kineWc
equaWon
CME at early stage
CKT Simulations
• A. Huang, Y. Jiang, S. Shi, J. Liao, and P. Zhuang, arXiv:1703.08856
• Y. Sun, C. M. Ko, and F. Li, Phys. Rev. C94, 045204 (2016);
Y. Sun and C.M. Ko Phys. Rev. C95, 034909 (2017)
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
• Central rapidity regime
• Longitudinal boost Invariance
• Proper time
• Bjorken velocity
t
z
Bjorken boost invariance (I)
• Dirac equation
– (proper time) and η (space rapidity) coordinates – Gauge:
– Spinor basis
Bjorken boost invariance (II)
• Boost invariance
– Assuming no η (space rapidity) dependence in gauge field
– Fourier transform
– y: momentum rapidity , η: space rapidity
• spinor depends on y-η
F. Gelis, K. KajanWe, and T. Lappi, Phys. Rev. C71, 024904 (2005)
F. Gelis and N. Tanji, JHEP 02, 126 (2016)
S. Ebihara, K. Fukushima, and SP, Phys.Rev. D96 (2017), 016016
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Bjorken boost invariance (II)
Ordinary boost invariant kinetic theory
• Central rapidity
• Longitudinal boost invariance (1+1 D expansion)
G. Baym, PLB (1984)
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Ordinary boost invariant kinetic theory
• Kine/c theory:
• Par/cle number conserva/on:
Charge density
System is expanded.
• Central rapidity
• Longitudinal expansion, homogenous in transverse direc/on
Boost invariance chiral kinetic theory (I)
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Boost invariance chiral kinetic theory(II)
We consider the Right-handed fermions only.
Without external fields
• Par/cle number
•
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Measurement with side-jump x ?
z
= z t
• When we boost f(z) back to z=0, because of side- jump,
The media in transverse plane is required.
• It is new!
Chiral circular displacement
x
y
z
• Assuming:
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Analogy to Thomas precession (I)
• Thomas precession:
For an accelerated object, besides the standard Lorentz boost,
it is rotating in lab frame.
• e.g. Thomas half
correction to spin-orbital interactions between electron
and nucleus in hydrogenic atoms.
Analogy to Thomas precession (II)
• 4-velocity form: vorticity (!!!)
• Is Chiral circular displacement (or side-jump)
related to the Thomas precession (or vorticity)?
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
Particle number conservation
• number density
•
•
CME, anomalous Hall current + Expansion in z direction
Side-jump CME Anomalous
Hall current
Summary
Shi Pu (Uni. of Tokyo) Workshop of QCD and QFT, Taipei 2017
