Fermion Tunneling Beyond Semiclassical Approximation
  Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in \cite{Majhi3} for the scalar particle, Hawking radiation as tunneling of Dirac particle through an event horizon is analysed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly. 
Bibhas Ranjan Majhi