Transport Properties of a spinon Fermi surface coupled to a U(1) gauge field

With the organic compound $\kappa$-(BEDT-TTF)$_2$-Cu$_2$(CN)$_3$ in mind, we consider a spin liquid system where a spinon Fermi surface is coupled to a U(1) gauge field. Using the non-equilibrium Green's function formalism, we derive the Quantum Boltzmann Equation (QBE) for this system. In this system, however, one cannot a priori assume the existence of Landau quasiparticles. We show that even without this assumption one can still derive a linearized equation for a generalized distribution function. We show that the divergence of the effective mass and of the finite temperature self-energy do not enter these transport coefficients and thus they are well-defined. Moreover, using a variational method, we calculate the temperature dependence of the spin resistivity and thermal conductivity of this system.