acta physica slovaca

Abstract: We consider renormalization group (RG) equations in field theories with broken symmetry. The key idea is to treat them like unbroken theories in an external field and absorb the symmetry breaking terms into the redefinition of parameters. Then, RG equations for the broken theory follow directly from those of unbroken one. A particular example of a supersymmetric gauge theory is considered in more detail.

Abstract: Approximate solutions for the gluon and ghost propagators as well as the running coupling in Landau gauge Yang-Mills theories are presented. These propagators obtained from the corresponding Dyson-Schwinger equations are in remarkable agreement with those of recent lattice calculations. The resulting running coupling possesses an infrared fixed point, $\alpha_S(0) = 8.92/N$ for all gauge groups SU($N$). Above one GeV the running coupling rapidly approaches its perturbative form.

Abstract: The latest electroweak precision data are analyzed assuming the existence of the fourth generation of leptons ($N, E$) and quarks ($U, D$), which are weakly mixed with the known three generations. If all four new particles are heavier than $Z$ boson, quality of the fit for the one new generation is as good as for the Standard Model (SM). In the case of neutral leptons with masses around 50 GeV (``partially heavy extra generations'') the minimum of $\chi^2$ is between one and two extra generations. SM prediction of light higgs is no more valid if new generations exist.

Abstract: We show that the renormalization group decimation of modern nucleon potential models to low momenta results in a unique nucleon interaction \vlk. This interaction is free of short-ranged singularities and can be used directly in many-body calculations. The renormalization group (RG) scaling properties follow directly from the invariance of the scattering phase shifts. We discuss the RG treatment of Fermi liquids. The RG equation for the scattering amplitude in the two particle-hole channels is given at zero temperature. The flow equations are simplified by retaining only the leading term in an expansion in small momentum transfers. The RG flow is illustrated by first studying a system of spin-polarized fermions in a simple model. Finally, results for neutron matter are presented by employing the unique low momentum interaction \vlk~as initial condition of the flow. The RG approach yields the amplitude for non-forward scattering, which is of great interest for calculations of transport properties and superfluid gaps in neutron star interiors. The methods used can also be applied to condensed matter systems in the absence of long-ranged interactions.

Abstract: Within the framework of exact renormalization group flow equations, a scale-dependent transformation of the field variables provides for a continuous translation of UV to IR degrees of freedom. Using the gauged Nambu-Jona-Lasinio model as an example, this translation results in a construction of partial bosonization at all scales. A fixed-point structure arises which makes it possible to distinguish between fundamental-particle and bound-state behavior of the scalar fields.

Abstract: The consequences of the renormalization group invariance in calculations of the ground state energy for models of confined quantum fields are discussed. The case of (1+1)D MIT quark bag model is considered in detail.

Abstract: We reanalyze deep inelastic scattering data of Bologna-CERN-Dubna-Munich-Saclay (BCDMS) Collaboration by including proper cuts of ranges with large systematic errors. We perform also fits of high statistic deep inelastic scattering data of BCDMS, SLAC, new muon (NM) and Berkeley-FNAL-Princeton (BFP) Collaborations taking the data separately and in combined way and find good agreement between these analyses. We extract the values of the QCD coupling constant $\alpha_s(M^2_Z)$ up to next-to-leading order level.

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Abstract: The Regge Calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The Discrete Regge Model employed in this work limits the choice of the link lengths to a finite number. For both theories there seems to be a discontinuous phase transition at positive gravitational coupling and a smooth transition at negative coupling. To construct a simple theory of quantum gravity with matter fields, we couple the four-dimensional Discrete Regge Model to Ising spins. We examined the phase transition of the spin system and the associated critical exponents. The results are obtained from finite-size scaling analyses of Monte Carlo simulations. We find consistency with the mean-field critical behavior of the Ising model on a static four-dimensional lattice. A main concern in lattice field theories is the existence of a continuum limit which requires the existence of a continuous phase transition. The second-order transition of the Ising model together with the second-order transition of the Regge skeleton at negative gravity coupling is such a candidate.

Abstract: We review the Batalin-Vilkovisky quantization procedure for Yang-Mills theory on a 2-point space.

Abstract: We consider the infrared quasi fixed point solutions of the one-loop renormalization group equations for the Yukawa couplings and soft supersymmetry breaking parameters in the Next-to-Minimal Supersymmetric Standard Model. Taking as input the top-quark and Z-boson masses, the values of the gauge coupling constants and the infrared quasi fixed points for Yukawa couplings and the soft parameters, the mass of the lightest Higgs boson is discussed.

Abstract: Non-decoupling properties of additional heavy degrees of freedom in the Higgs sector of the Two-Higgs-doublet extension of the Standard model are discussed in a particular case of production of a pair of longitudinaly polarized $W$-bosons in the $e^+e^-$ annihilation.

Abstract: The $\pi^0\gamma\gamma$ vertex is used as an explicit example of the subtleties connected with the application of {\it equation of motion\/} within Chiral Perturbation Theory at the order $\mathcal{O}(p^6)$.

Abstract: An introduction to the theory of critical behavior at Lifshitz points is given, and the recent progress made in applying the field-theoretic renormalization group (RG) approach to $\phi^4$ $n$-vector models representing universality classes of $m$-axial Lifshitz points is surveyed. The origins of the difficulties that had hindered a full two-loop RG analysis near the upper critical dimension for more than 20 years and produced long-standing contradictory $\epsilon$-expansion results are discussed. It is outlined how to cope with them. The pivotal role the considered class of continuum models might play in a systematic investigation of anisotropic scale invariance within the context of thermal equilibrium systems is emphasized. This could shed light on the question of whether anisotropic scale invariance implies an even larger invariance, as recently claimed in the literature.

Abstract: We give an introduction to the critical dynamics and review recent progress made within the field theoretic renormalization group approach. Our main concern are liquids and superfluids. Two loop calculations are inevitable for different reasons in both cases. Calculations of the field theoretic functions take into account the decomposition of the dynamical vertex functions into the static vertex functions and genuine dynamical parts. This makes possible a complete two loop calculation of the critical dynamics near the superfluid transition of $^3$He-$^4$He mixtures (model F'). As result we obtain the flow equations of the dynamical parameters and the amplitude functions of the various transport coefficients, which governs the nonasymptotic and non universal temperature dependence. From a reduction of our expressions we obtain the field theoretic functions of model F describing the critical dynamics of the supefluid transition in pure $^4$He and of model C correcting long standing results.

Abstract: The functional renormalization group method is used to take into account the vacuum polarization around localized bound states generated by external potential. The application to Atomic Physics leads to improved Hartree-Fock and Kohn-Sham equations in a systematic manner within the framework of the Density Functional Theory. Another application to Condensed Matter Physics consists of an algorithm to compute quenched averages with or without Coulomb interaction in a non-perturbative manner.

Abstract: Large order asymptotic behaviour of renormalization constants in the minimal subtraction scheme for the $\phi ^4$ $(4-\epsilon)$ theory is discussed. Well-known results of the asymptotic $4-\epsilon $ expansion of critical indices are shown to be far from the large order asymptotic value. A {\em convergent} series for the model $\phi ^4$ $(4-\epsilon)$ is then considered. Radius of convergence of the series for Green functions and for renormalisation group functions is studied. The results of the convergent expansion of critical indices in the $4-\epsilon $ scheme are revalued using the knowledge of large order asymptotics. Specific features of this procedure are discussed.

Abstract: We report on some results concerning the effects of cubic anisotropy and quenched uncorrelated impurities on multicomponent spin models. The analysis of the six-loop three-dimensional series provides an accurate description of the renormalization-group flow.

Abstract: We investigate the critical properties of $d=3$-dimensional magnetic systems with quenched defects, correlated in $\varepsilon_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-\varepsilon_d$ dimensions. Our renormalization group (RG) calculations are performed in the minimal subtraction scheme. We analyze the 2-loop RG functions for different fixed values of the parameter $\varepsilon_d$. To this end, we apply the Chisholm-Borel resummation technique and report the numerical values of the critical exponents for the new universality class.

Abstract: We study the conditions under which the critical behaviour of a three-dimensional $mn$-vector model is non-trivial, i.~e. its universal characteristics do not belong to an $O(m)$ universality class. In the calculations we rely on the field-theoretical renormalization group approach in different regularization schemes. We use adjusted resummation and extended analysis of the series for renormalization-group functions which are known for the model in high orders of perturbation theory. As a result we build the regions in $m-n$ plane where non-trivial critical behaviour is realized.

Abstract: A Renormalization Group approach to disordered spin systems is presented, based on a real space coarse graining of the overlap distribution. Universality classes are defined through generalized disorder distribution, thus including a large set of models such as Ising ferromagnet, Gaussian and $Z_2$ spin glasses, fully frustrated models. The relations between $Z_2$ gauge models and spin glasses find a natural framework within this context. The approach is supported by Monte Carlo renormalization group computations in three dimensions. Precise estimates of the critical temperature and indexes in the difficult 3D case are also obtained with moderate computer time.

Abstract: We report on some results concerning the off-equilibrium response and correlation functions and the corresponding fluctuation-dissipation ratio for a purely dissipative relaxation of an $O(N)$ symmetric vector model (Model A) in $d$ dimensions below the upper critical dimension. The scaling behaviour of these quantities is analyzed and the associated universal functions are given at first order in $\epsilon=4-d$ in the high-temperature phase and at criticality. A non trivial limit of the fluctuation-dissipation ratio is found at criticality.

Abstract: In this article, we review basic facts about disordered systems, especially the existence of many metastable states and and the resulting failure of dimensional reduction. Besides techniques based on the Gaussian variational method and replica-symmetry breaking (RSB), the functional renormalization group (FRG) is the only general method capable of attacking strongly disordered systems. We explain the basic ideas of the latter method and why it is difficult to implement. We finally review current progress for elastic manifolds in disorder.

Abstract: A progress in constructing renormalization group symmetries by means of a regular approach is described. A basic sketch of general ideas of the algorithm is followed by several illustrations for solutions of boundary value problems in plasma physics.