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# Chiral Kinetic Theory with small mass corrections and quantum coherent states

*by*

### Cristina Manuel

**Abstract:**

In systems made up of massless fermions, the hydrodynamical equations have to include the effects of the chiral quantum anomaly. The so-called anomalous hydrodynamics might be derived from a microscopic approach, chiral kinetic theory, which contains quantum corrections to classical transport equations. We explain how quantum effects might be incorporated in transport theory, using effective field theory techniques. We also study the effect of a small fermion mass in the formulation of the chiral kinetic theory. Besides the left-handed and right-handed distribution functions components needed in the massless case, distribution functions describing quantum coherent mixtures of left and right-handed fermions are also required, which also enter in the chiral anomaly equation. We study how these two different sets of functions are related by Lorentz symmetry transformations.

**Keywords:**

Relativistic transport theory, semiclassical expansions, effective field theory, chiral anomaly.