Lorentz invariance in chiral kinetic theory

Area of Science:

• Theoretical physics
• Particle physics
• Quantum field theory

Background:

• Lorentz invariance is a fundamental symmetry in physics.
• Understanding classical actions is key to quantum field theory.
• Helicity of massless particles has unique properties.

Purpose of the Study:

• To investigate the realization of Lorentz invariance in classical actions.
• To explore modifications to Lorentz transformations for massless spin-1/2 particles.
• To connect classical actions to quantum phenomena like the chiral-vortical effect.

Main Methods:

• Analyzing the classical action of massless spin-1/2 particles.
• Deriving modified Lorentz transformations.
• Examining implications for angular momentum conservation and kinetic theory.
• Calculating contributions to the chiral-vortical effect.
• Taking the classical limit of a Weyl particle's path integral.

Main Results:

• Lorentz invariance is realized nontrivially, modifying standard transformations.
• A novel shift orthogonal to boost and momentum vectors is identified.
• This shift ensures angular momentum conservation and introduces nonlocality (side jumps) in kinetic theory.
• Two-thirds of the chiral-vortical effect is linked to magnetic moment coupling from Lorentz invariance.
• The classical action is derived from the path integral of a Weyl particle.

Conclusions:

• The study reveals a deeper, nontrivial structure of Lorentz invariance in classical physics.
• Modified transformations have significant consequences for particle collisions and kinetic theory.
• The findings provide a classical explanation for a portion of the chiral-vortical effect.