A possibility for grand unification and non-Higgs mass generation in a Nambu-Jona-Lasinio-like theory of fermions interacting with current metric field

Grand unification possibilities in Nambu-Jona-Lasinio-like models are studied. To address the problem of vector boson masses and nonrenormalizability of the theory, algebraic formalism encompassing the effective action, Schwinger-Keldysh path integral, and Bogoliubov-Parasiuk-Hepp-Zimmerman renormalization is constructed. A new NJL-like model: the theory of current metric field interacting with fermions is proposed. Bosonization in this model can produce massless vector bosons under certain conditions which makes it a candidate grand unified theory. Both Higgs and non-Higgs effects can contribute to particle masses.