arXiv subjects

D. G. Pak

Publications and source records attributed to D. G. Pak.

At least 19 recordsLinked to original sources

arXiv2020

Color structure of quantum SU(N) Yang-Mills theory

Color confinement is the most puzzling phenomenon in the theory of strong interaction based on a quantum SU(3) Yang-Mills theory. The origin of color confinement supposed to be intimately related to non-perturbative features of the non-Abelian gauge theory, and touches very foundations of the theory. We revise basic concepts underlying QCD concentrating mainly on concepts of gluons and quarks and color structure of quantum states. Our main idea is that a Weyl symmetry is the only color symmetry which determines all color attributes of quantum states and physical observables. We construct an ansatz for classical Weyl symmetric dynamical solutions in SU(3) Yang-Mills theory which describe one particle color singlet quantum states for gluons and quarks. Abelian Weyl symmetric solutions provide microscopic structure of a color invariant vacuum and vacuum gluon condensates. This resolves a problem of existence of a gauge invariant and stable vacuum in QCD. Generalization of our consideration to SU(N) (N=4,5) Yang-Mills theory implies that the color confinement phase is possible only in SU(3) Yang-Mills theory.

hep-th↗

arXiv2020

Color confinement and color singlet structure of quantum states in Yang-Mills theory

We consider two fundamental long-standing problems in quantum chromodynamics (QCD): the origin of color confinement and structure of a true vacuum and color singlet quantum states. There is a common belief that resolution to these problems needs a knowledge of a strict non-perturbative quantum Yang-Mills theory and new ideas. Our principal idea in resolving these problems is that structure of color confinement and color singlet quantum states must be determined by a Weyl symmetry which is an intrinsic symmetry of the Yang-Mills gauge theory, and by properties of a selected class of solutions satisfying special requirements. Following this idea we construct for the first time a space of color singlet one particle quantum states for primary gluons and quarks and reveal the structure of color confinement in quantum Yang-Mills theory. As an application we demonstrate formation of physical observables in a pure QCD, pure glueballs.

hep-th↗

arXiv2018

Microscopic vacuum structure in a pure QCD

We propose a class of stationary color magnetic solutions in a pure quantum chromodynamics (QCD) which are stable under gluon quantum fluctuations. This resolves a long-standing problem of microscopic description of a stable non-trivial vacuum in a pure QCD. The solutions represent fixed points in a full space of gauge fields under Weyl group transformations. An important feature of the solutions is the phenomenon of Weyl invariant Abelian projection and Abelian dominance in the vacuum structure. As an application of our approach we consider an effective Lagrangian of pure Abelian glueballs in the presence of vacuum gluon condensate.

hep-th↗

arXiv2018

Axially-symmetric stationary solutions in a pure SU(3) QCD

We propose an ansatz for a class of regular axially-symmetric solutions in SU(3) QCD. After averaging over time period the solution can be treated as a non-topological monopole-antimonopole pair. We demonstrate that QCD Lagrangian on the space of such solutions is explicitly Weyl symmetric and reduces to a generalized phi^4 model with four independent fields. All solutions possess quantum stability under vacuum gluon fluctuations.

hep-th↗

arXiv2018

Stable spherically symmetric monopole field background in a pure QCD

We consider a stationary spherically symmetric monopole like solution with a finite energy density in a pure quantum chromodynamics (QCD). The solution can be treated as a static Wu-Yang monopole dressed in time dependent field corresponding to off-diagonal gluons. We have proved that such a stationary monopole field represents a background vacuum field of the QCD effective action which is stable against quantum gluon fluctuations. This resolves a long-standing problem of existence of a stable vacuum field in QCD and opens a new avenue towards microscopic theory of the vacuum.

hep-th↗

arXiv2017

On microscopic structure of the QCD vacuum

We propose a new class of regular stationary axially symmetric solutions in a pure QCD which correspond to monopole-antimonopole pairs at macroscopic scale. The solutions represent vacuum field configurations which are locally stable against quantum gluon fluctuations in any small space-time vicinity. This implies that the monopole-antimonopole pair can serve as a structural element in microscopic description of QCD vacuum formation through the monopole pair condensation.

hep-th↗

arXiv2017

Quantum stability of non-linear wave type solutions with intrinsic mass parameter in QCD

The problem of existence of a stable vacuum field in a pure quantum chromodynamics (QCD) is revised. Our approach is based on using classical stationary non-linear wave type solutions with intrinsic mass scale parameter. Such solutions can be treated as quantum mechanical wave functions describing massive spinless states in quantum theory. We verify whether non-linear wave type solutions can form a stable vacuum field background within the framework of effective action formalism. We demonstrate that there is a special class of stationary generalized Wu-Yang monopole solutions which are stable against quantum gluon fluctuations.

hep-th↗

arXiv2017

Gauge invariant gluon spin operator for spinless non-linear wave solutions

We consider non-linear wave type solutions with mass scale parameter and vahished canonical spin density operator in a pure SU(2) quantum chtomodynamics (QCD). A new stationary solution which can be treated as a system of static Wu-Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered non-linear wave type solutions have common features: presence of a mass scale parameter, non-vanishing projection of the color magnetic field along the propagation direction and zero spin density. The last property requires revision of the gauge invariant definition of the spin density operator which supposed to be massless vector field in the classical theory. We construct a gauge invariant definition of the classical gluon spin density which is unique and Lorentz frame independent.

hep-th↗

arXiv2015

Non-monopole magnetic solutions in the Weinberg-Salam model

The structure of finite energy non-monopole solutions with azimuthal magnetic flux of topological origin is studied in the pure bosonic sector of the Weinberg-Salam model. Applying a variational method we have found simple magnetic field configurations which minimize the energy functional and possess energies of order 1 TeV. Such configurations correspond to composite bound states of W, Z and Higgs bosons with essentially less energy in comparison to monopole like particles supposed to be found at LHC.

hep-ph↗

arXiv2015

On finite energy monopole solutions in Weinberg-Salam model

We study the problem of existence of finite energy monopole solutions in the Weinberg-Salam model starting with a most general ansatz for static axially-symmetric electroweak magnetic fields. The ansatz includes an explicit construction of field configurations with various topologies described by the monopole and Hopf charges. We introduce a unique SU(2) gauge invariant definition for the electromagnetic field. It has been proved that the magnetic charge of any finite energy monopole solution must be screened at far distance. This implies non-existence of finite energy monopole solutions with a non-zero total magnetic charge. In a case of a special axially-symmetric Dashen-Hasslacher-Neveu ansatz we revise the structure of the sphaleron solution and show that sphaleron represents a non-trivial system of monopole and antimonopole with their centers located in one point. This is different from the known interpretation of the sphaleron as a monopole-antimonopole pair like Nambu's "dumb-bell". In general, the axially-symmetric magnetic field may admit a helical structure. We conjecture that such a solution exists and estimate an upper bound for its energy, E_{bound}=4.65 TeV.

hep-th↗

arXiv2013

Monopoles without magnetic charges: Finite energy monopole-antimonopole configurations in CP1 model and restricted QCD

We propose a new type of regular monopole-like field configuration in quantum chromodynamics (QCD) and CP^1 model. The monopole configuration can be treated as a monopole-antimonopole pair without localized magnetic charges. An exact numeric solution for a simple monopole-antimonopole solution has been obtained in CP^1 model with an appropriate potential term. We suppose that similar monopole solutions may exist in effective theories of QCD and in the electroweak standard model.

hep-th↗

arXiv2013

Knot topology in QCD

We consider topological structure of classical vacuum solutions in quantum chromodynamics. Topologically non-equivalent vacuum configurations are classified by non-trivial second and third homotopy groups for coset of the color group SU(N) (N=2,3) under the action of maximal Abelian stability group. Starting with explicit vacuum knot configurations we study possible exact classical solutions as vacuum excitations. Exact analytic non-static knot solution in a simple CP^1 model in Euclidean space-time has been obtained. We construct an ansatz based on knot and monopole topological vacuum structure for searching new solutions in SU(2) and SU(3) QCD. We show that singular knot-like solutions in QCD in Minkowski space-time can be naturally obtained from knot solitons in integrable CP^1 models. A family of Skyrme type low energy effective theories of QCD admitting exact analytic solutions with non-vanishing Hopf charge is proposed.

hep-th↗

arXiv2013

Exact knot solutions in a generalized Skyrme-Faddeev model

We propose a generalized Skyrme-Faddeev type theory with an additional scalar field. In a special case of model parameters one has a theory which admits exact knot solutions given by a class of exact toroidal solitons from Aratyn-Ferreira-Zimerman (AFZ) integrable CP1 model. In a general case the theory admits an exact knot solution for a unit Hopf charge. For higher Hopf charges we perform numeric analysis of the solutions and obtain estimates for the knot energies using energy minimization procedure based on ansatz with AFZ field configurations and with rational functions. We show that AFZ configurations provide a better approximate solutions. The corresponding knot energies are in a good agreement with a standard law for the low energy bound, E_H\simeq Q_H^{3/4}.

hep-th↗

arXiv2012

Weyl symmetric structure of QCD vacuum

We consider Weyl symmetric structure of the classical vacuum in quantum chromodynamics. In the framework of formalism of gauge invariant Abelian projection we show that classical vacuums can be constructed in terms of Killing vector fields on the group SU(3). Consequently, homotopic classes of Killing vector fields determine the topological structure of the vacuum. In particular, the second homotopy group π_2(SU(3)/U(1)\times U(1)) describes all topologically non-equivalent vacuums which are classified by two topological numbers. For each given Killing vector field one can construct six vacuums forming Weyl sextet representation. An interesting feature of SU(3) gauge theory is that it admits a Weyl symmetric vacuum represented by a linear superposition of the six vacuums from the Weyl vacuum sextet. A non-trivial manifestation of Weyl symmetry is demonstrated on monopole solutions. We construct a family of finite energy monopole solutions in Yang-Mills-Higgs theory which includes Weyl monopole sextet. From the analysis of the classical vacuum structure and monopole solutions we conjecture that a similar Weyl symmetric vacuum structure can be realized in quantum theory.

hep-th↗

arXiv2012

On gauge invariant nucleon spin decomposition

A non-uniqueness problem of gauge invariant separation of quark and gluon contributions to nucleon spin is considered. We show that there is a wide number of gauge invariant spin decompositions each of them reduces to the canonical one in a special gauge. A class of physical gauge equivalent nucleon spin decompositions is selected by requirements of consistence with helicity notion described within E(2) little group representation theory and with gluon helicity Δg measured in experiment.

hep-ph↗

arXiv2012

Consistent gauge invariant nucleon spin decomposition

We consider a non-uniqueness problem of gauge invariant nucleon spin decomposition. A gauge invariant decomposition with a generalized Coulomb constraint for the physical gluon has been constructed. The decomposition scheme is consistent with the concept of helicity in non-Abelian gauge theory. We provide an explicit representation for the gauge invariant Abelian projection which implies further separation of gluon into binding and valence parts.

hep-ph↗

arXiv2012

Lorentz gauge theory as a model of emergent gravity

We consider a class of Lorentz gauge gravity theories within Riemann-Cartan geometry which admits a topological phase in the gravitational sector. The dynamic content of such theories is determined only by the contortion part of the Lorentz gauge connection. We demonstrate that there is a unique Lagrangian that admits propagating spin one mode in correspondence with gauge theories of other fundamental interactions. Remarkably, despite the R^2 type of the Lagrangian and non-compact structure of the Lorentz gauge group, the model possesses rather a positive-definite Hamiltonian. This has been proved in the lowest order of perturbation theory. This implies further consistent quantization and leads to renormalizable quantum theory. It is assumed that the proposed model describes possible mechanism of emergent Einstein gravity at very early stages of the Universe due to quantum dynamics of contortion.

gr-qc↗

arXiv2011

Vacuum tunneling in gravity

Topologically non-trivial vacuum structure in gravity models with Cartan variables (vielbein and contortion) is considered. We study the possibility of vacuum space-time tunneling in Einstein gravity assuming that the vielbein may play a fundamental role in quantum gravitational phenomena. It has been shown that in the case of RP3 space topology the tunneling between non-trivial topological vacuums can be realized by means of Eguchi-Hanson gravitational instanton. In Riemann-Cartan geometric approach to quantum gravity the vacuum tunneling can be provided by means of contortion quantum fluctuations. We define double self-duality condition for the contortion and give explicit self-dual configurations which can contribute to vacuum tunneling amplitude.

hep-th↗