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.
Time Flow and Flavor Mixing in the Flavor Spin Theory
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abstract
We show that unlike the SM in the flavor spin theories (theories with non- Euclidean/pseudo-unitary signature of the kinematic quadratic term of the Lagrangian) the Yukawa mass matrices are not arbitrary. This restricts the possible textures of both lepton and quark flavor mixing matrices to the experimentally observed form and reduces the number of real mixing parameters by two. In addition, some pairs of elements of V_CKM and separately U_PMNS are forced to have the same absolute values, which is experimentally confirmed within the error bounds. Apart from the flavor mixing the change in the signature imprints no changes in the SM.
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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.