# Resummation for the Field-theoretical Derivation of the Negative Magnetoresistance

## TL;DR

This paper provides a detailed field-theoretical derivation of negative magnetoresistance in quark matter, linking it to chiral anomaly and showing how electric conductivity varies with magnetic field strength.

## Contribution

It introduces a microscopic, field-theoretical approach to derive electric conductivity under magnetic fields, elucidating the transition from quadratic to linear dependence.

## Key findings

- Conductivity changes from quadratic to linear with increasing magnetic field.
- The formulation supports the interpretation of negative magnetoresistance as a chiral anomaly.
- Provides a general methodology for analyzing transport coefficients in magnetic fields.

## Abstract

We show detailed derivation of the electric conductivity of quark matter at finite temperature and density under a magnetic field. We especially focus on the longitudinal electric conductivity along the magnetic direction and establish the field-theoretical description of the negative magnetoresistance as observed in chiral materials. With increasing magnetic field our microscopic calculation leads to changing behavior from approximately quadratic to asymptotically linear dependence of the electric conductivity, while the magnetic dependence is quadratic in the conventional relaxation time approximation. The presented formulation founds a firm basis for the physical interpretation of the negative magnetoresistance as manifestation of the chiral anomaly, as well as it offers general methodology applicable for various transport coefficients.