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.     

Anomalous nonconservation of baryon number in decays of heavy fermions in electroweak theory

It is shown that the inclusion of a heavy fermionic doublet in the standard model of electroweak interactions can lead to the formation of nontopological soliton states of two different types. The effects of the complicated vacuum structure lead to instability of the soliton states with respect to anomalous decay with nonconservation of the fermionic quantum numbers. If the fermion mass exceeds a critical value m_cr10–18 TeV, then, besides the formation of the soliton state, there exists a possibility of rapid anomalous decay of the bare fermion.Institute of Nuclear Physics, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 21–36, January, 1992.     

A (2+1)-Dimensional Gauge Model with Electrically Charged Fermions

We consider a (2+1)-dimensional gauge theory with a nonzero fermion density and an initial Chern–Simons topological term, whose Lorentz invariance is spontaneously broken in a certain Lorentz reference frame by the generation of a constant homogenous magnetic field. We propose interpreting the number =±1, which characterizes the two nonequivalent representations of Dirac matrices in 2+1 dimensions, as a quantum number that explicitly describes the spin of the fermion. In particular, this interpretation allows determining the vacuum state of the model in a constant homogenous magnetic field as the state whose fermion and spin numbers are equal to zero.     

Quantum string theory in the space of states in an indefinite metric

The quantum string theory in the indefinite (pseudo-Hilbert) Fock representation is considered. It is shown that all anomalies in the four-dimensional theory of an open bosonic string are canceled for a particular choice of the vacuum state. Then the algebra of the reparametrization symmetry (in the covariant approach) and the algebra of rotations (in the light-cone gauge) become closed. The indefiniteness of the space of states leads to some nonphysical properties of the theory. Modifications of the model under consideration, which are necessary to construct a more realistic theory, are discussed.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 2, pp. 213–228, May, 1996.Translated by L. O. Chekhov.     

Condensation of fermion pairs in a domain

We consider a gas of fermions at zero temperature and low density, interacting via a microscopic two-body potential which admits a bound state. The particles are confined to a domain with Dirichlet boundary conditions. Starting from the microscopic BCS theory, we derive an effective macroscopic Gross–Pitaevskii (GP) theory describing the condensate of fermion pairs. The GP theory also has Dirichlet boundary conditions. Along the way, we prove that the GP energy, defined with Dirichlet boundary conditions on a bounded Lipschitz domain, is continuous under interior and exterior approximations of that domain.     

Gauge invariance of the dimension-two condensate in the Yang-Mills theory

We demonstrate the gauge independence of the dimension-two vacuum condensate in the Yang-Mills theory using a noncommutative theory technique.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 1, pp. 3–8, April, 2005.     

Instantons and gravitation theory

Some problems related to using nonperturbative quantization methods in theories of gauge fields and gravitation are studied. The unification of interactions is considered in the context of the geometric theory of gauge fields. The notion of vacuum in the unified interaction theory and the role of instantons in the vacuum structure are considered. The relation between the definitions of instantons and the energymomentum tensor of a gauge field and also the role played by the vacuum solutions to the Einstein equations in the definition of vacuum for gauge fields are demonstrated. The Schwarzschild solution, as well as the entire class of vacuum solutions to the Einstein equations, is a gravitational instanton even though the signature of the space-time metric is hyperbolic. Gravitation, oncluding the Einstein version, is considered a special case of an interaction described by a non-Abelian gauge field. Translated from Teoreticheskaya i Matematicheskaya. Fizika. Vol. 115, No. 2, pp. 312–320, May. 1998.     

可压Navier-Stokes方程真空状态的动力学行为

本文主要考虑了一维可压Navier-Stokes方程真空状态的动力学行为.对于任意的熵弱解,如果初始状态不存在真空,我们证明了密度函数关于时间和空间变量是连续的且对于任意时间它是处处为正的.同时,我们还得到了含有间断连接的真空状态的整体熵弱解的存在性,结果显示其真空区域以代数速率被压缩,并在有限时间内消失.     

On the algebraic geometry ofS-duality

This paper deals with algebro-geometric questions arising in the verification of theS-duality conjecture for supersymmetric Yang-Mills quantum field theories in the four-dimensional case. We describe all the cases for the gauge groups of rank 1 and 2, where the Gell-Man-Law beta-function is either zero or negative, and point out some series of such cases for gauge groups of arbitrary rank. Realization of one of these series on the complex projective plane demonstrates a relationship with exceptional bundles. Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 163–178, February, 1997. Translated by S. K. Lando     

Non-existence of vortices in the small density region of a condensate

In this paper, we answer a question raised by Lev Pitaevskii and prove that the ground state of the Gross-Pitaevskii energy describing a Bose-Einstein condensate in a rotationally symmetric trap at low rotation does not have vortices in the low density region. Therefore, the first ground state with vortices has its vortices in the bulk. In fact we prove something stronger, which is that the ground state for the model at low and moderate rotations is equal to the ground state in a condensate with no rotation. This is obtained by proving that for small rotational velocities, the ground state is multiple of the ground state with zero rotation. We rely on sharp bounds of the decay of the wave function combined with weighted Jacobian estimates.     

Nonanticommutative deformations of <Emphasis Type="Italic">N</Emphasis>=(1, 1) supersymmetric theories

We discuss chirality-preserving nilpotent deformations of the four-dimensional N=(1, 1) Euclidean harmonic superspace and their implications in N=(1, 1) supersymmetric gauge and hypermultiplet theories. For the SO(4) × SU(2)-invariant deformation, we present nonanticommutative Euclidean analogues of the N=2 gauge multiplet and hypermultiplet off-shell actions.As a new result, we consider a specific nonanticommutative hypermultiplet model with the N=(1, 0) supersymmetry. It involves free scalar fields and interacting right-handed spinor fields.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 235–251, February, 2005.     

Theory of a spatially periodic bose condensate in the weakly nonideal Bose gas model

The possibility of constructing the theory of a spatially periodic Bose condensate in the weakly nonideal Bose gas model is studied. The concept of quasi means and the related separated Bose condensate method are used to derive equations for determining the spatially periodic order parameter for zero temperature at which the contribution of quasiparticles to the thermodynamics of the boson system can be neglected. One-period solutions of these equations are found. Questions of thermodynamic stability are considered for a spatially periodic Bose condensate. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 1, pp. 152–176, October, 2000.     

Influence of the pseudoscalar condensate gradient on the cooling regime of compact stars

We consider the processes in compact stars that arise during the potential formation of a pseudoscalar condensate in finite volumes. We do not propose specific hypotheses about the nature of this condensate. Considering that in the regions with a changing pseudoscalar density, photon propagation can be described in the framework of Maxwell–Chern–Simons electrodynamics, we find the reflection/transmission coefficients for regions with different densities. We study the fermion spectrum in the presence of an axial field considering the pseudoscalar condensate gradient. We also study the influence of the modified photon and fermion spectra on the cooling process of compact stars.     

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.     

Non-Abelian tensor gauge fields

A recently proposed extension of Yang-Mills theory contains non-Abelian tensor gauge fields. The Lagrangian has quadratic kinetic terms, as well as cubic and quartic terms describing nonlinear interaction of tensor gauge fields with the dimensionless coupling constant. We analyze the particle content of non-Abelian tensor gauge fields. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity 2 and 0. We introduce interaction of the non-Abelian tensor gauge field with fermions and demonstrate that the free equation of motion for the spinor-vector field correctly describes the propagation of massless modes of helicity 3/2. We have found a new metric-independent gauge invariant density which is a four-dimensional analog of the Chern-Simons density. The Lagrangian augmented by this Chern-Simons-like invariant describes the massive Yang-Mills boson, providing a gauge invariant mass gap for a four-dimensional gauge field theory.     

Observables and critical behaviour in fermionic matrix models

We review the properties of adjoint fermion one-, two-, and generic D-dimensional matrix models at large N. We derive and solve the complete sets of loop equations for the correlators of these models and examine the ensuing critical behavior. The topological 1/N-expansions are also constructed, and we discuss the applications of these matrix models to string theory and induced gauge theories.Work supported in part by the Natural Sciences and Engineering Research Council of Canada.Work supported in part by a University of British Columbia Graduate Fellowship.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 1, pp. 78–122, July, 1995.     

The null energy condition and cosmology

Field theories that violate the null energy condition (NEC) are of interest both for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter w < −1. We consider two recently proposed models that violate the NEC. The ghost condensate model requires higher-derivative terms in the action, and this leads to a heavy ghost field and energy unbounded from below. We estimate the rates of particle decay and discuss possible mass limitations to protect the stability of matter in the ghost condensate model. The nonlocal stringy model that arises from a cubic string field theory and exhibits a phantom behavior also leads to energy unbounded from below. In this case, the energy spectrum is continuous, and there are no particle-like excitations. This model admits a natural UV completion because it comes from superstring theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 3–12, April, 2008.     

Chiral Bag Model with Constituent Quarks: Topological and Nontopological Solutions

We consider a three-phase modification of the hybrid chiral bag model involving the intermediate constituent quark phase along with the asymptotic freedom and hadronization phases. We find self-consistent solutions of the equations of the model in 1+1 dimensions with the fermion vacuum polarization effects taken into account. We study the renormalized total energy of the bag as a function of parameters characterizing the geometry of the bag and its topological (baryon) charge. We show that for a nonzero topological charge, there exists an entire series of configurations that are local minimums of the total energy of the bag and contain all the three phases, whereas in the nontopological case, the bag energy minimum corresponds to zero sizes of the domain of the asymptotic freedom phase.     

Phase transitions and theta vacuum energy

The analytic behaviour of θ-vacuum energy is related to the existence of phase transitions in QCD and ℂP ^N sigma models. The absence of singularities different from Lee-Yang zeros only permits ∧ cusp singularities in the vacuum energy density and never ∨ cusps. This fact, together with the Vafa-Witten diamagnetic inequality, provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vector-like gauge theories and ℂP ^N sigma models. However, this property does not exclude the existence of a first phase transition at θ = π or a second order phase transition at θ = 0, which might be very relevant for interpretation of the anomalous behaviour of the topological susceptibility in the ℂP¹ sigma model.