Abstract
We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the O(1/μ) expansion, but in agreement with the equation derived in on-shell effective field theory upon identification of cutoff. By using reparametrization transformation properties of the effective theory, we show that the difference in kinetic equations from two approaches are in fact expected. It is simply due to different choices of degree of freedom by effective theory and field theory. We also show that they give equivalent description of the dynamics of chiral fermions.
Highlights
The chiral kinetic equation (CKE) has been derived in different ways
We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the O(1/μ) expansion, but in agreement with the equation derived in on-shell effective field theory upon identification of cutoff
We find the resulting CKE differs from the counterpart from field theory approach in high order terms in the 1/μ expansion
Summary
High density effective theory (HDET) [35–37] is very useful in describing low energy dynamics. It is constructed in a simple manner by identifying the heavy degrees of freedom and integrating them out from the theory as irrelevant modes. This process generates a non-local effective Lagrangian, which can be expanded in terms of large momentum. We derive HDET Lagrangian for massless fermions valid in the vicinity of Fermi surface. This is not new but is included for completeness. Subsection is devoted to the derivation of Wigner function and its equation of motion, which eventually leads to dispersion relation and transport equation
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