Condensation of pairs formed by spatially separated electrons and holes in a system of two isolated graphene layers is studied beyond the mean-field approximation. Suppression of the screening of the pairing interaction at large distances, caused by the appearance of the gap, is considered self-consistently. A mutual positive feedback between the appearance of the gap and the enlargement of the interaction leads to a sharp transition to a correlated state with a greatly increased gap above some critical value of the coupling strength. At a coupling strength below the critical value, this correlation effect increases the gap approximately by a factor of 2. The maximal coupling strength achievable in experiments is close to the critical value. This indicates the importance of correlation effects in closely spaced graphene bilayers at weak substrate dielectric screening. Another effect beyond the mean-field approximation considered is the influence of vertex corrections on the pairing, which is shown to be very weak.

The superconducting pairing of electrons in doped graphene owing to in-plane and outof-plane phonons is considered. It is shown that the structure of the order parameter in the valley space substantially affects conditions of the pairing. Electron-hole pairing in a graphene bilayer in the strong coupling regime is also considered. Taking into account retardation of the screened Coulomb pairing potential shows a significant competition between the electron-hole direct attraction and their repulsion owing to virtual plasmons and single-particle excitations.

The structure of bound magnetic polarons in an antiferromagnetic matrix is studied in the framework of two-dimensional (2D) and three-dimensional (3D) Kondo-lattice models in the double exchange limit (JH ≫ t). The conduction electron is bound by a nonmagnetic donor impurity and forms a ferromagnetic core of the size about the electron localization length (bound magnetic polaron). We find that the magnetic polaron produces rather long-range extended spin distortions of the antiferromagnetic background around the core. In a wide range of distances, these distortions decay as 1/r 2 and 1/r 4 in 2D and 3D cases, respectively. In addition, the magnetization of the core is smaller than its saturation value. Such a magnetic polaron state is favorable in energy in comparison to usually considered one (saturated core without extended distortions).

Nonlocal quantum theory of one-component scalar field in D-dimensional Euclidean spacetime is studied in representations of S-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant g in the form of an infrared smooth function of argument x for space without boundary. Nonlocality is given by evolution of Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter l. By representation of the S-matrix in terms of abstract functional integral over primary scalar field, the S form of a grand canonical partition function is found. And, by expression of S-matrix in terms of the partition function, the representation for S in terms of basis functions is obtained. Derivations are given for discrete case where basis functions are Hermite functions, and for continuous case where basis functions are trigonometric functions. The obtained expressions for the S-matrix are investigated within the framework of variational principle based on Jensen inequality. And, by the latter, the majorant of S (more precisely, of − ln S) is constructed. Equations with separable kernels satisfied by variational function q are found and solved, yielding results for both the polynomial theory ϕ 4 (with suggestions for ϕ 6 ) and the nonpolynomial sine-Gordon theory. A new definition of the S-matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are obtained and illustrated numerically, with plots of variational functions q and corresponding majorants for the S-matrices of the theory. For simplicity of numerical calculation: the D = 1 case is considered, and propagator for the free theory G is in the form of Gaussian function typically in the Virton-Quark model, although the obtained analytical inferences are not limited to these particular choices in principle. The formulation for nonlocal QFT in momentum k space of extra dimensions with subsequent compactification into physical spacetime is discussed, alongside the compactification process. Recently, the discovery of Higgs boson, the last SM element in energy domain, where existence is most natural, occurred: Notably, by the remarkable event confirming validity of SM, a quantum-trivial local quantum theory of scalar field is, after all, not quantum trivial if the SM is a sector of a non-Abelian gauge theory; analogous to QED event.Groundbreaking of Supersymmetric Non-Abelian QFTs as well as Integrable QFTs [1-9] in earnest search for quantum theory of gravity will naturally complement superstring theory. Under such sophistication for superstring theory, which is almost surely strongest pick for fundamental theory of nature, the ultimate truth, it will not be impossible to view all QFTs as effective (low-energy) theory given by renormalizable and nonrenormalizable QFTs, respectively. In other words, every field theory will be a limit in superstring theory. Hypothetically, bosonic string...