FERMIONIC ENTROPY IN 2D BLACK-HOLE

The Dirac equation for a Dirac field in a 2D black hole with a Schwarz schild-like metric is solved. Contrary to the bosonic eigensolution, t he fermionic one is found to be divergent on the horizon, but it is no t too singular and can be normalized in the inner product.'t Hooft's b oundary condition, which is suitable for scalar bosons, is found not t o be applicable to the fermionic eigensolutions. In order to discretiz e the spectrum, a ''quasi-periodic'' boundary condition is first propo sed, and the fermionic effective Hamiltonian operator H-F is shown to be self-adjoint with this ''quasi-periodic'' boundary condition. The r esult shows that the divergence in the fermionic entropy has the same form as that in the bosonic one, except that the coefficient is differ ent. Thus the original divergence in the bosonic entropy cannot be can celled by a supersymmetric Bose-Fermi cancellation.