Keldysh spinors, despite their negative action and Hamiltonian, reduce in the non-relativistic limit to the same positive-definite Pauli Hamiltonian as Dirac spinors, up to a charge sign.
Kamenev, Field theory of non-equilibrium systems, Cambridge University Press, 2023
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The Non-Relativistic Limit of Keldysh Spinors
Keldysh spinors, despite their negative action and Hamiltonian, reduce in the non-relativistic limit to the same positive-definite Pauli Hamiltonian as Dirac spinors, up to a charge sign.