  By a singular gauge transformation, the quasi-particle transport in the mixed
state of high T_{c} cuprates is mapped into charge-neutral composite Dirac
fermion moving in short-range correlated random scalar and long-range
correlated vector potential. A fully quantum mechanical approach to
longitudinal and transverse thermal conductivities is presented. The
semi-classical Volovik effect is presented in a quantum mechanical way. The
quasi-particle scattering from the random magnetic field which was completely
missed in all the previous semi-classical approaches is the dominant scattering
mechanism at sufficiant high magnetic field. The implications for experiments
are discussed.
