International Journal of Modern Physics A

This article has been retracted. A statement of retraction is published in Int. J. Mod. Phys. A, Volume 28, Issue 16 (2013) http://dx.doi.org/10.1142/S0217751X13930019.

A new version of this article will be published in Int. J. Mod. Phys. A, Volume 28, Issue 16 (2013) Article No. 1330026, DOI: S0217751X13300263.

We construct the states of maximal localization taking into account a modification of the commutation relation between position and momentum operators to all orders of the minimum length parameter. To first-order, the algebra we use reproduces the one proposed by Kempf, Mangano and Mann. It is emphasized that a minimal length acts as a natural regulator for the theory, thus eliminating the otherwise ever appearing infinities. So, we use our results to calculate the first correction to the Casimir effect due to the minimal length. We also discuss some of the physical consequences of the existence of a minimal length, culminating in a proposal to reformulate the very concept of "position measurement."

The perturbative renormalization group (RG) treatment of the Ginzburg–Landau model is reconsidered based on the Feynman diagram technique. We derive RG flow equations, exactly calculating all vertices appearing in the perturbative RG transformation of the φ⁴ model up to the ε³ order of the ε-expansion. The Fourier-transformed two-point correlation function G(k) has been considered. Although the ε-expansion of X(k) = 1/G(k) is well defined on the critical surface, we have revealed an inconsistency with the exact rescaling of X(k), represented as an expansion in powers of k at k →0. This new result can serve as a basis to challenge the correctness of the ε-expansion-based perturbative RG method.

Self-similarity of jet production in pp and collisions is studied in the framework of z-scaling. Inclusive jet transverse momentum distributions measured by the STAR Collaboration at RHIC, the CDF and D∅ Collaborations at Tevatron and the CMS and ATLAS Collaborations at LHC are analyzed. The experimental spectra are compared with next-to-leading order QCD calculations in p_T- and z-presentations. It is shown that self-similar features of jet cross-sections manifested by the z-scaling give strong restriction on the scaling function ψ(z) at high z. New results on energy and angular independence and asymptotic behavior of ψ(z) are discussed. The obtained results are considered as confirmation of self-similarity of jet production, fractality of hadron structure and locality of constituent interactions at small scales.

The temperature induced phase transition is investigated in the one-component scalar field ϕ⁴ model on the lattice. Using the GPU cluster a huge amount of Monte Carlo simulation data is collected for a wide interval of coupling values. This gives a possibility to determine the low bound on the coupling constant λ₀ when the transition happens and investigate its type. We found that for the values of λ close to this bound a weak-first-order phase transition takes place. It converts into a second-order one with the increase of λ. A comparison with the results obtained in analytic and numeric calculations by other authors is given.

A model for electroweak unification of quarks and leptons, in a gauge group SU_C(3) × SU(4) × U_X(1) is constructed. The model requires, three generations of quarks and leptons which are replicas (mirror) of the standard quarks and leptons. The gauge group SU(4) × U_X(1) is broken in such a way so as to reproduce standard model and to generate heavy masses for the vector bosons , the leptoquarks and mirror fermions. It is shown lower limit on mass scale of mirror fermions is , E^- being the lightest mirror fermion coupled to Z boson. As the universe expands, the heavy matter is decoupled at an early stage of expansion and may be a source of dark matter. Leptoquarks in the model connect the standard model and mirror fermions. Baryon genesis in our universe implies antibaryon genesis in mirror universe.

Basing upon experience from performing double-dimensional reduction of the D = 11 supermembrane on AdS₄ × S⁷ background to Type IIA superstring on AdS₄ × ℂℙ³ we introduce Kaluza–Klein (partial) κ-symmetry gauge as a vanishing condition of the contributions to the D = 11 supervielbein components tangent to D = 10 space–time that are proportional to the differential of the coordinate parametrizing compact 11th space–time dimension identified with the supermembrane worldvolume compact dimension. For AdS₄ × S⁷ supermembrane Kaluza–Klein gauge removes half Grassmann coordinates associated with eight space–time supersymmetries, broken by the AdS₄ × ℂℙ³ superbackground, by imposing D = 3 (anti-)Majorana condition on them. The consideration relies on the realization of osp(4|8) isometry superalgebra of the AdS₄ × S⁷ superbackground as superconformal algebra. Requiring further vanishing of the D = 10 dilaton leaves in the sector of broken supersymmetries just two Grassmann coordinates organized into D = 3 (anti-)Majorana spinor that defines minimal SL(2, ℝ)-covariant extension of the OSp(4|6)/(SO(1, 3) × U(3)) sigma-model. Among four possibilities of such a minimal extension we consider in detail one, that corresponds to picking out D = 3 Majorana coordinate related to broken Poincaré supersymmetry, and show that the AdS₄ × ℂℙ³ superstring equations of motion in this partial κ-symmetry gauge are integrable. Also the relation between the OSp(4|6)/(SO(1, 3) × U(3)) sigma-model and the AdS₄ × ℂℙ³ superstring is revisited.