Title: Ward identities for charge and heat currents of particle-particle and particle-hole pairs,
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.