The Negative Action Keldysh Spinors

Abstract: 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.