Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory

Abstract

International audienceWe derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function

On-shell effective field theory: A systematic tool to compute power corrections to the hard thermal loops

“…[28]. For the computation of different physical observables dominated by the contribution of almost on-shell fermions it is convenient to construct an EFT where the role of the quantum fluctuations is clearly singled out.…”

“…Then after integrating out the H (1) v and H (2) v fields (see Ref. [28] for details) one obtains the following effective Lagrangian…”

“…[28], is a systematic and powerful tool to extract power corrections to the HTLs. As an example we focus here in studying the retarded polarization tensor of QED.…”

Electromagnetic fields and anomalous transports in heavy-ion collisions—a pedagogical review

“…There are a variety of methods to derive Eq. (30) from microscopic quantum field theory [2, 15, 102-104, 115, 117, 119, 120, 136, 137], mesoscopic kinetic theory [138][139][140][141][142][143][144][145][146][147][148][149][150][151][152], to macroscopic hydrodynamic approach [22,[153][154][155][156][157][158]. Here we pick up one of these derivations given by Fukushima, Kharzeev, and Warringa [115] because it is elementary and easy to see the relation between CME and the lowest Landau level and the axial anomaly.…”

Chiral transport of neutrinos in supernovae: Neutrino-induced fluid helicity and helical plasma instability

“…For completeness and generality, we first review the kinetic theory (and hydrodynamics in the next section) for charged chiral particles [6][7][8][9][10][11][12][13], with the emphasis on the corrections due to the chirality. The kinetic theory and hydrodynamics for neutral neutrinos can be obtained by simple modifications later.…”