  We discuss quantization of Dirac spinors with action which is the negative of
the standard action. Using the Keldysh QFT formulation, we show that the
standard quantization of such Keldysh spinors results in the Hamiltonian
bounded from above and in S-matrix for backwards in time scattering. The
alternative quantization produces the standard Hamiltonian bounded from below
and the standard S-matrix for forwards in time scattering. When the two masses
are equal, the sum of their actions describes the standard Keldysh
out-of-time-order correlators. When both Keldysh and Dirac spinors are present
in a QFT, the standard Fock space is augmented by negative energy states, while
its positive and the negative subspaces share the same vacuum state. In absence
of gravity the Dirac and the Keldysh spinors do not interact and positive and
negative energy states do not exchange quanta with non-zero energy. If Keldysh
spinors exist in Nature, then the Universe would consist of bosonic and
fermionic particles that are described by both positive and negative Fock
energy states with a single vacuum state that cannot be crossed from either
side. Such a scenario could explain the non-observation of dark energy/dark
matter except via classical gravity.
