  A theory of dispersionless Andreev bound states on surfaces of time-reversal
invariant unconventional superconductors is presented. The generalized
criterion for the dispersionless Andreev bound state is derived from the
bulk-edge correspondence, and the chiral spin structure of the dispersionless
Andreev bound states is argued from which the Andreev bound state is
stabilized. Then we summarize the criterion in a form of index theorems. The
index theorems are proved in a general framework to certify the bulk-edge
correspondence. As concrete examples, we discuss (i) dxy-wave superconductor
(ii) px-wave superconductor, and (iii) noncentrosymmetric superconductors. In
the last example, we find a peculiar time-reversal invariant Majorana fermion.
The time-reversal invariant Majorana fermion shows an unusual response to the
Zeeman magnetic field, which can be used to identify it experimentally.
