Ward Identities for Hall Transport

TL;DR

This paper derives Ward identities in 2+1 dimensions linking Hall viscosities, conductivities, and angular momentum, applicable to various physical systems and conditions, including external fields and temperature effects.

Contribution

It introduces a unified derivation of Ward identities relating Hall transport coefficients and angular momentum in diverse 2+1D systems, extending previous relations.

Findings

Derived identities linking Hall viscosities, conductivities, and angular momentum.

Applicable to relativistic and non-relativistic systems at various temperatures.

Includes cases with external magnetic fields and viscous drag.

Abstract

We derive quantum field theory Ward identities based on linear area preserving and conformal transformations in 2+1 dimensions. The identities relate Hall viscosities, Hall conductivities and the angular momentum. They apply both for relativistic and non relativistic systems, at zero and at finite temperature. We consider systems with or without translation invariance, and introduce an external magnetic field and viscous drag terms. A special case of the identities yields the well known relation between the Hall conductivity and half the angular momentum density.