# Ward identities for charge and heat currents of particle-particle and particle-hole pairs

## TL;DR

This paper derives Ward identities for charge and heat currents in particle-particle and particle-hole pairs, clarifying their role as constraints from conservation laws and addressing misconceptions in superconducting fluctuation studies.

## Contribution

It provides the first correct interpretation of Ward identities for heat currents and applies these to critique existing inconsistent results in high-Tc superconductor research.

## Key findings

- Correct interpretation of heat current Ward identity
- Identification of inconsistencies in previous superconducting fluctuation studies
- Establishment of exact constraints on current-vertex functions

## Abstract

The Ward identities for the charge and heat currents are derived for particle-particle and particle-hole pairs. They are the exact constraints on the current-vertex functions imposed by conservation laws and should be satisfied by consistent theories. While the Ward identity for the charge current of electrons is well established, that for the heat current is not understood correctly. Thus the correct interpretation is presented. On this firm basis the Ward identities for pairs are discussed. As the application of the identity we criticize some inconsistent results in the studies of the superconducting fluctuation transport and the transport anomaly in the normal state of high-Tc superconductors.