The functional integral in the Hubbard model

In a new functional integral approach proposed for the model, we find the regime with a deformed integration measure in which the standard integral is replaced with the Jackson integral. We indicate the relation to a $p$-adic functional integral. For the magnetic and electronic subsystems in the effective functional that results from the operator formulation of the Hubbard model, we find the two-parametric quantum derivative resulting in the appearance of the quantum $SU_{rq}(2)$ group. We establish the relation to the one-parametric quantum derivative and to the standard derivative.