Magnetic catalysis in a P-even, chiral-invariant three-dimensional model with four-fermion interaction

We study how an external magnetic field H affects the phase structure of a P-even, chiral-invariant three-dimensional model of field theory with a four-fermion interaction. An arbitrarily small, but nonzero, magnetic field induces the spontaneous breaking of the initial symmetry (the magnetic catalysis phenomenon). Depending on the values of the coupling constants, the model vacuum is either P-even or chiral invariant for H≠0. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 2, pp. 323–338, August, 2000.     

Determination of scalar meson masses in QCD-inspired quark models

We compare two QCD-inspired quark models with four-fermion interaction (with and without the remnant coupling to low-energy gluons) in the regime of dynamical chiral symmetry breaking (DCSB). The first one, the Nambu-Jona-Lasinio (NJL) model, ensures the factorization of scalar and pseudoscalar meson poles in correlators, the well-known Nambu relation between the scalar meson mass and the dynamical quark mass, m_σ=2m_dyn, and the residual chiral symmetry in coupling constants characteristic for the linear σ-model. The second one, the gauge NJL model (GNJL), happens to be qualitatively different from the NJL model, namely, the Nambu relation is not valid, and the factorization of light meson poles does not entail the residual chiral symmetry, i.e., it does not result in a linear σ-model. The more complicated DCSB pattern in the GNJL model is fully explained in terms of excited meson states with the same quantum numbers. The asymptotic restrictions on parameters of scalar and pseudoscalar meson states are derived from the requirement of chiral symmetry restoration at high energies. Bibliography: 13 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 245, 1997, pp. 5–21.     

Two-Point Correlators of Composite Higgs Fields and Chiral Symmetry Restoration

We consider the effective quasilocal quark model with two composite Higgs doublets in strong coupling (polycritical) regime below the chiral symmetry breaking energy scale _CSB. The two-point correlators of scalar and pseudoscalar Higgs fields are calculated. The adjustment of their asymptotics at high energies allows one to implement the chiral symmetry restoration in correspondence to the operator product expansion in QCD-like (technicolor, topcolor) models. The requirement of chiral symmetry restoration (CSR) at high energies above the _CSB yields some bounds on parameters of (composite) Higgs particles and underlying effective quasilocal quark models. Bibliography: 26 titles.     

Dynamical CP-violation in quasilocal quark models at nonzero quark chemical potential

We consider the Quasilocal Quark Model of Nambu-Jona-Lasinio type as an effective theory of non-perturbative QCD with scalar-pseudoscalar four-quark interaction which includes derivatives in fields at finite quark chemical potential. In the presence of a strong attraction in the scalar channel, the chiral symmetry is spontaneously broken and, as a consequence, composite meson states are generated. For special configurations of coupling constants, the dynamical CP-violation in the pseudoscalar sector can appear as a result of complexity of the dynamical mass function generated at some value of quark density. Bibliography: 25 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 335, 2006, pp. 5–21.     

Effective fermion models near a tricritical point

We consider the class of fermion models with a momentum cutoff Λ and an interaction containing derivatives. For the quasilocal fermion model with two coupling constants near a tricritical point, we classify the solutions of mass-gap equations for different values of coupling constants. The mass spectrum of the scalar excitations in the vicinity of the tricritical point is derived and it is found that two scalar exitations always arise when at least one of the constants exceeds its critical value. The mass formation for scalar bound states induced by static gluon fields (gluon condensates) is investigated. Bibliography 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 5–19. Translated by V. A. Andrianov.     

Effective fermion models with dynamical symmetry breaking

Effective many-fermion models with finite momentum cutoff in the regime of dynamical symmetry breaking are considered as low-energy approximation to the action of quantum chromodynamics. The quasilocal interaction vertices responsible for the formation of dynamic fermion mass are classified for these models in the near-critical region of coupling constants. It is shown that in four-dimensional space not only the 4-fermion interaction but also vertices with six and eight fermion fields and any number of derivatives are also important. In the mean field approximation an equation is derived for the critical surface for the coupling constants of the effective fermion action. The role of the leading interaction vertices in forming the physical parameters that do not depend on the momentum cutoff is discussed.St Petersburg State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 6–18, January, 1993.     

Standard model of fermions on the domain wall in five-dimensional space-time

The mechanism of generation of the Standard Model for fermions on the domain wall in five-dimensional space-time is presented. As a result of self-interaction of five-dimensional fermions and gravity induced by matter fields, in the strong coupling regime, in the model there arises a spontaneous translational symmetry breaking, which leads to localization of light particles on a 3 + 1-dimensional domain wall (“3-brane”) that is embedded into a five-dimensional anti-de Sitter space-time (AdS₅). Appropriate low-energy, effective action, classical kink-like vacuum configurations for the gravity and scalar fields are investigated. Mass spectra for light composite particles and their coupling constants interaction in ultra-low-energy, which localize on the brane, are explored. We establish estimates of characteristic scales and constants interactions of the model and also a relation between the bulk five-dimensional gravitational constant, curvature of AdS₅ space-time, and brane Newton’s constants. The induced cosmological constant on the brane exactly vanishes in all orders of the theory perturbation. We find out that scalar interaction is strongly suppressed at ultra-low-energy, and the brane fluctuations (branons) are suitable “sterile” canditates for explanation of the phenomenon of Dark Matter. Bibliography: 21 titles. Dedicated to the 100th birthday of M. P. Bronstein __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 5–29.     

Vacuum decay of non-Abelian vortices

This note is a case study of a general SU(2) gauge vortex model where the two Higgs multiplets are in the adjoint representation of the gauge group and the Higgs potential energy density contains cross interaction terms The vacuum decay of finite-energy solutions is proved and the existence of a non-trivial solution is established. Moreover, for a special choice of the parameter region, the occurrence of a non-linear desingularization phenomenon is observed.     

CP Violation in the models of fermion localization on a domain wall (brane)

We briefly review the mechanism of fermion localization on a domain wall (“thick brane”) generated by a topologically nontrivial vacuum configuration of scalar fields. We propose an extension of the scalar field coupling to fermions that endows the fermions with an axial mass. In the case of several flavors and fermion generations, this extension can lead to the appearance of the Standard Model Cabibbo-Kobayashi-Maskawa matrix. We also consider a model with two scalar doublets that ensures an additional mechanism of CP-parity violation.     

Vacuum structure of the(\bar \psi \psi )_3^2 -model,accounting for the magnetic field and chemical potentialψ) 3 2 -model,accounting for the magnetic field and chemical potential

The phase structure of a (2 + 1)-dimensional field theory with four-fermion interaction is investigated, accounting for the external magnetic field H and chemical potential μ. The existence of the critical curve μ = μ_c(H) dividing the manifold of points (μ, H) into two regions is demonstrated. In one of the regions, the vacuum is chiral-symmetric and in the other, the symmetry is spontaneously broken. The behavior of the critical curve at large and small values of the external field is analyzed.     

Complete cosmological model based on an asymmetric scalar Higgs doublet

Theoretical and Mathematical Physics - We study a complete cosmological model based on an asymmetric scalar doublet represented by the classical and phantom scalar Higgs fields. Moreover, we remove...     

Magnetic Susceptibility of the Random One- Dimensional Transverse Ising Model

We study the 1- dimensional Ising model with random coupling constants in the presence of a transverse magnetic field h. In the nonrandom (translationally invariant) case it is known that there is a value of h for which the magnetic susceptibility diverges logarithmically. We demonstrate that in the random case this logarithmic divergence is smoothed out into an infinitely differentiable essential singularity.     

Synchronization criteria in complex dynamical networks with nonsymmetric coupling and multiple time-varying delays

In this article, we consider a generalized complex dynamical network model with nonsymmetric coupling, and the dynamics of each node has a different time-varying delay. Criteria of exponential synchronization are derived in terms of linear matrix inequalities for the model by constructing suitable Lyapunov functionals. The obtained outcomes are different from those in the current literature, in which the complex dynamical networks are coupling symmetrically and delays are fixed constants. Moreover, the given sufficient conditions extend current available results and are verifiable. A numerical example is provided to illustrate the efficiency of the derived outcome.     

On Bogoliubov's method in superconductivity

The Frölich Hamiltonian, with the addition of the electron-boson interaction of the fourth degree in fermion operators, is studied. The Hamiltonian takes into account the exchange interactions of the magnetic moments of the conduction electrons. The boson spectrum consists of the normal modes of coupled phonon-magnon oscillations. Using the Bogobliubov method in the theory of superconductivity and a generalized canonic transformation, a system of equations describing the mutual compensation of dangerous (i.e., leading to divergences) dingrams corresponding to the creation of two (bivertexes) and of four (tetravertexes) electron excitations from vacuum is obtained. The bivertex compensation equation, modified by a four-fermion interaction, indicates the possibility of an effective increase in the electron-boson coupling constant and an increase in the superconductive energy gap. Numerical investigation of the obtained system of equations was carried out. The considerable increase in the energy gap was revealed in comparison with the Frölich model.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 1, pp. 129–141, April, 1996.     

The n-Wave Procedure and Dimensional Regularization for the Scalar Field in a Homogeneous Isotropic Space

We obtain expressions for the vacuum expectations of the energy–momentum tensor of the scalar field with an arbitrary coupling to the curvature in an N-dimensional homogeneous isotropic space for the vacuum determined by diagonalization of the Hamiltonian. We generalize the n-wave procedure to N-dimensional homogeneous isotropic space–time. Using the dimensional regularization, we investigate the geometric structure of the terms subtracted from the vacuum energy–momentum tensor in accordance with the n-wave procedure. We show that the geometric structures of the first three subtractions in the n-wave procedure and in the effective action method coincide. We show that all the subtractions in the n-wave procedure in a four- and five-dimensional homogeneous isotropic space correspond to a renormalization of the coupling constants of the bare gravitational Lagrangian.     

Can broken rotational invariance be reconciled with inflation?

Motivated by claims of broken rotational invariance in the WMAP data, a number of models have appeared in the literature realizing this effect through vector field(s) with a nonvanishing spatial vacuum expectation value. We discuss why many such models have ghost instabilities.     

VERTEX FUNCTIONS AND GENERALIZED NORMAL-ORDERING BY TRIPLE SYSTEMS IN NON-LINEAR SPINOR FIELD MODELS

Triple systems, more precisely ternary rings, are closely related to Yang-Baxter symmetries and integrable models. We seek for a possibility to employ triple systems in effective non-linear spinor field theories and explore the nature of q-deformation from an unconventional point of view. Starting with a non-parameter-dependent, that is non-Yang-Baxterian, triple product, we derive at first the BCS interaction. Turning to deformed symmetries leads in some sense to a regular vertex function. The Yang-Baxter matrix is seen to govern the generalized normal-ordering. The connection to the effect of running coupling constants is outlined. Our model shares much features with the recently discussed anisotropic effective local interactions introduced to obtain QCD confinement. A geometrically motivated discussion of the physics behind q-symmetries is given.     

A P-Brane vindication of the two Higgs-doublet minimally super-symmetric standard model and related issues

The two-Higgs doublet MSSM predicts three neutral and two charged Higgs particles. The present work gives a vindication of this model based on a P-Brane model in eleven dimensions. Subsequently, we give alternative derivations using various ideas from the theory of maximally symmetric spaces and E-Infinity theory.     

Three-dimensional Gross-Neveu model in external chromomagnetic fields at finite temperature

A (2+1)-dimensional four-fermion theory at finite temperature in external chromomagnetic fields that model a vacuum gluon condensate is considered. The critical properties of the theory are investigated, and the dependence of the fermion mass on the external field is also found.Institute of High Energy Physics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 3, pp. 391–401, December, 1994.