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On the basis of the linear response transport theory, the general expressionsfor the thermoelectric transport coefficients, such as thermoelectric power(S), Nernst coefficient (\nu), and thermal conductivity (\kappa), are derivedby using the Fermi liquid theory. The obtained expression is exact as for themost singular term in terms of 1/\gamma_k^* (\gamma_k^* being the quasiparticledamping rate). We utilize the Ward identities for the heat current which isderived by the local energy conservation law. Based on the derived expressions,we can calculate various thermoelectric transport coefficients within theframework of the Baym-Kadanoff type conserving approximation. Thus, the presentexpressions are very useful for studying the strongly correlated electrons suchas high-Tc superconductors, organic metals, and heavy Fermion systems, wherethe current vertex corrections are expected to play important roles. By usingthe derived expression, we calculate the thermal conductivity \kappa in afree-dispersion model up to the second-order with respect to U. We find that itis slightly enhanced due to the vertex correction for the heat current,although the vertex correction for electron current makes the conductivity(\sigma) of this system diverge, reflecting the absence of the Umklapp process.Comment: 22 pages, 11 figures; accepted for publication in PR

physical review. b, condensed matter

General formula for the thermoelectric transport phenomena based on Fermi liquid theory: Thermoelectric power, Nernst coefficient, and thermal conductivity