New functional representation in superspace for the Hubbard model

Description of conductivity steps in polymer and other materials by functions of p‐adic argument

“…As a rule, low-dimensional systems are in the strong correlation regime. In [5,6] a novel approach to many-electron systems based on nonlinear functional integral has been developed. The presence of nonlinear terms leads to the induction in the system of some quantum symmetry given by the Hopf algebra when strong Coulomb repulsion exist in system.…”

“…In conclusion, we showed that the proposed p-adic function qualitatively well describes the two type of conduction as a function of voltage in polymer TA-PPE. Let us briefly give a general scheme for obtaining the effective functional for the Hubbard model, proposed in the papers [5,6] and further developed in recent papers . We start from the Hubbard model, written in the usual creation and annihilation operators:…”

“…Next we use a functional formulation of many-electron systems, proposed in work [5]. According to this approach, the evolution operator between initial and final states is given by the following functional integral with action, expressed through effective functional, which is calculated (2) using supercoherent state.…”

The functional integral in the Hubbard model

“…We briefly describe the general scheme for constructing the effective functional for the Hubbard model proposed in [10] and recently further developed, for example, in [17]. We begin with the Hubbard model written in terms of the standard creation-annihilation operators,…”

“…This nonlinearity allows segregating those terms that provide quantum derivatives determining generators of the quantum algebra in expressions belonging to the universal enveloping algebra. In [10], we introduced the approximation in which radius vectors of vector fields were independent of the dynamical field coordinates. This assumption is equivalent to the approximation in which the values of the fields that correspond to the Casimir operators and to the invariants of the classical groups SU (2) and SU (1, 1) in our formulation are coordinate independent.…”