Kinetic theory with Berry curvature from quantum field theories

Abstract

A kinetic theory can be modified to incorporate triangle anomalies and the chiral magnetic effect by taking into account the Berry curvature flux through the Fermi surface. We show how such a kinetic theory can be derived from underlying quantum field theories. Using the new kinetic theory, we also compute the parity-odd correlation function that is found to be identical to the result in the perturbation theory in the next-to-leading order hard dense loop approximation.

From Chirality of Neutrinos to Supernovae

“…The current and energy-momentum tensor are expressed by the neutrino distribution function f = f (t, x, p) as [5,7] …”

“…For more details of the chiral kinetic theory, see Refs. [3][4][5][6]. In supernovae, there are not only neutrinos, but also ordinary matter (nuclei and electrons), which must also be incorporated in the transport theory.…”

“…In the language of kinetic theory for neutrinos, these topological effects can be captured by the notion of the Berry curvature. The kinetic framework with Berry curvature corrections for chiral fermions (not limited to neutrinos) is now referred to as the chiral kinetic theory [3][4][5][6].…”

Chiral transport of neutrinos in supernovae

“…Since parity is violated in the microscopic theory, parity must also be violated in the kinetic theory (and hydrodynamics if applicable) for left-handed neutrinos. Although such chiral effects have been completely ignored in the conventional transport theory in astrophysics, the modified kinetic theory and hydrodynamics that take into account these effects have been constructed in the areas of nuclear and particle physics and are now called the chiral kinetic theory [4][5][6][7] and chiral (or anomalous) hydrodynamics [8], respectively.…”

Primordial Generation of Magnetic Fields

“…The resulting theory can reproduce the triangle anomaly and provide the descriptions for the chiral magnetic and chiral vorticity effects [10]. In this work we apply the Berry curvature modified kinetic theory to the chiral plasma for the study of generation of primordial magnetic field.…”