Lorentz invariance in chiral kinetic theory.
We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-1/2 particle with definite helicity. We find that the ordinary Lorentz transformation is modified by a shift orthogonal to the boost vector and the particle momentum. The shift ensures angular momentum conservation in particle collisions and implies a nonlocality of the collision term in the Lorentz-invariant kinetic theory due to side jumps. We show that 2/3 of the chiral-vortical effect for a uniformly rotating particle distribution can be attributed to the magnetic moment coupling required by the Lorentz invariance. We also show how the classical action can be obtained by taking the classical limit of the path integral for a Weyl particle.
Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA.
Jing-Yuan
JY
Chen
Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA.
Dam T
DT
Son
Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA and Physics Department, University of Illinois at Chicago, Chicago, Illinois 60607, USA.
Mikhail A
MA
Stephanov
Physics Department, University of Illinois at Chicago, Chicago, Illinois 60607, USA and RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA.
Ho-Ung
HU
Yee
Physics Department, University of Illinois at Chicago, Chicago, Illinois 60607, USA.
Yi
Y
Yin