arXiv subjects
Publications and source records attributed to V. Dzhunushaliev.
We calculate dimensional reduction of gravitational flux tube solutions in the scheme of Kaluza-Klein theory. The fifth dimension is compacified to a region of Planck size. Assuming the width of the tube to be also Planck size we obtain string-like object with physical fields originated from an initial 5D metric. The dynamics of these fields is inner one.
A variation of Hawking's idea about Euclidean origin of a nonsingular birth of the Universe is considered. It is assumed that near to zero moment $t = 0$ fluctuations of a metric signature are possible.
Confinement in non-Abelian gauge theories, such as QCD, is often explained using an analogy to type II superconductivity. In this analogy the existence of the ``Meissner'' effect for quarks with respect to the QCD vacuum is an important element. Here we show that using the ideas of Abelian projection it is possible to arrive at an effective London equation from a non-Abelian gauge theory. (London's equation gave a phenomenological description of the Meissner effect prior to the Ginzburg-Landau or BCS theory of superconductors). The Abelian projected gauge field acts as the E&M field in normal superconductivity, while the remaining non-Abelian components form a gluon condensate which is described via an effective scalar field. This effective scalar field plays a role similar to the scalar field in Ginzburg-Landau theory.
An approximate model of a spacetime foam is presented. It is supposed that in the spacetime foam each quantum handle is like to an electric dipole and therefore the spacetime foam is similar to a dielectric. If we neglect of linear sizes of the quantum handle then it can be described with an operator containing a Grassman number and either a scalar or a spinor field. For both fields the Lagrangian is presented. For the scalar field it is the dilaton gravity + electrodynamics and the dilaton field is a dielectric permeability. The spherically symmetric solution in this case give us the screening of a bare electric charge surrounded by a polarized spacetime foam and the energy of the electric field becomes finite one. In the case of the spinor field the spherically symmetric solution give us a ball of the polarized spacetime foam filled with the confined electric field. It is shown that the full energy of the electric field in the ball can be very big.
It is offered to consider monopoles in Abelian Projection as quantum excitations which are solutions of the quantized Yang-Mills equations. According to the Heisenberg quantization method these equations are equivalent an infinite set of equations for Green's functions. A procedure for cutting off these infinite series of differential equations after some assumptions is offered. The received equations are identical to equations describing a dyon.
Within the context of the Abelian Projection of QCD monopole-like quantum excitations of gauge fields are studied. We start with certain classical solutions, of the SU(2) Yang-Mills field equations, which are not monopole-like and whose energy density diverges as $r \to \infty$. These divergent classical solutions are then quantized using a modified version of Heisenberg's quantization technique for strongly interacting, nonlinear fields. The modified Heisenberg quantization technique leads to a system of equations with mixed quantum and classical degrees of freedom. By applying a Feynman path integration over the quantum degrees of freedom the quantum-averaged solution gives a nondivergent, monopole-like configuration after Abelian Projection.
Monopole field configurations have been extensively studied in both Abelian and non-Abelian gauge theories. The question of the quantum corrections to these systems is a difficult one, since the classical monopoles have non-perturbatively large couplings, which makes the standard, perturbative methods for calculating quantum corrections suspect. Here we apply a modified version of Heisenberg's quantization technique for strongly interacting, nonlinear fields to a classical solution of the SU(3) Yang-Mills field equations. This classical solution is not monopole-like and has an energy density which diverges as $r \to \infty$. However, the quantized version of this solution has a monopole-like far field, and a non-divergent energy density as $r \to \infty$. This may point to the conclusion that monopoles may arise not from quantizing classical monopole configurations, but from quantizing field configurations which at the classical level do not appear monopole-like.
The multidimensional gravity on the principal bundle with the SU(2) gauge group is considered. The numerical investigation of the spherically symmetric metrics with the center of symmetry is made. The solution of the gravitational equations depends on the boundary conditions of the ``SU(2) gauge potential'' (off-diagonal metric components) at the symmetry center and on the type of symmetry (symmetrical or antisymmetrical) of these potentials. In the chosen range of the boundary conditions it is shown that there are two types of solutions: wormhole-like and flux tube. The physical application of such kind of solutions as quantum handles in a spacetime foam is discussed.
In this article we use the idea of algorithmic complexity (AC) to study various cosmological scenarios, and as a means of quantizing the gravitational interaction. We look at 5D and 7D cosmological models where the Universe begins as a higher dimensional Planck size spacetime which fluctuates between Euclidean and Lorentzian signatures. These fluctuations are governed by the AC of the two different signatures. At some point a transition to a 4D Lorentzian signature Universe occurs, with the extra dimensions becoming ``frozen'' or non-dynamical. We also apply the idea of algorithmic complexity to study composite wormholes, the entropy of blackholes, and the path integral for quantum gravity.
An approximate model of the spacetime foam is offered in which a quantum handle (wormhole) is a 5D wormhole-like solution. Neglecting the linear sizes of the wormhole throat we can introduce a spinor field for an approximate and effective description of the foam. The definition of the spinor field can be made by a dynamic and non-dynamic ways. In the first case some field equations are used and the second case leads to superspace. It is shown that : the spacetime with the foam is similar to a dielectric with dipoles and supergravity theories with a non-minimal interaction between spinor and electromagnetic fields can be considered as an effective model for the spacetime foam.
A geometrical interpretation of Grassmannian anticommuting coordinates is given. They are taken to represent an indefiniteness inherent in every spacetime point on the level of the spacetime foam. This indeterminacy is connected with the fact that in quantum gravity in some approximation we do not know the following information : are two points connected by a quantum wormhole or not ? It is shown that: (a) such indefiniteness can be represented by Grassmanian numbers, (b) a displacement of the wormhole mouth is connected with a change of the Grassmanian numbers (coordinates). In such an interpretation of supersymmetry the corresponding supersymmetrical fields must be described in an invariant manner on the background of the spacetime foam.
In this article we investigate the metric signature as a non-differentiable ({\it i.e.} discrete as opposed to continuous) degree of freedom. The specific model is a vacuum 7D Universe on the principal bundle with an SU(2) structural group. An analytical solution is found which to a 4D observer appears as a flat Universe with a fluctuating metric signature, and frozen extra dimensions with an SU(2) instanton gauge field. A piece of this solution with linear size of the Planck length ($\approx l_{Pl}$) can be considered as seeding the quantum birth of a regular Universe. A boundary of this piece can initiate the formation of a Lorentzian Universe filled with the gauge fields and in which the extra dimensions have been ``frozen''.
It is assumed that in some sense the High-T$_c$ superconductivity is similar to the quantum chromodynamics (QCD). This means that the phonons in High-T$_c$ superconductor have the strong interaction between themselves like to gluons in the QCD. At the experimental level this means that in High-T$_c$ superconductor exists the nonlinear sound waves. It is possible that the existence of the strong phonon-phonon interaction leads to the confinement of phonons into a phonon tube (PT) stretched between two Cooper electrons like a hypothesized flux tube between quark and antiquark in the QCD. The flux tube in the QCD brings to a very strong interaction between quark-antiquark, the similar situation can be in the High-T$_c$ superconductor: the presence of the PT can essentially increase the binding energy for the Cooper pair. In the first rough approximation the PT can be approximated as a nonrelativistic string with Cooper electrons at the ends. The BCS theory with such potential term is considered. It is shown that Green's function method in the superconductivity theory is a realization of discussed Heisenberg idea proposed by him for the quantization of nonlinear spinor field. A possible experimental testing for the string approximation of the Cooper pair is offered.
A recent investigation of SU(2) Yang-Mills theory found several classical solutions with bad behaviour at infinity : one of the potential components oscillated and another tended to infinity. In this paper we apply an idea due to Heisenberg about the quantization of strongly interacting nonlinear fields to these classical singular solutions. We find that this quantization procedure eliminates the bad long distance features while retaining the interesting short distance aspects of these solutions.
An approximate model of the spacetime foam is offered in which each quantum handle (wormhole) is a 5D wormhole-like solution. A spinor field is introduced for an effective description of this foam. The topological handles of the spacetime foam can be attached either to one space or connect two different spaces. In the first case we have a wormhole with the quantum throat and such object can demonstrate a model of preventing the formation the naked singularity with relation $e > m$. In the second case the spacetime foam looks as a dielectric with quantum handles as dipoles. It is supposed that supergravity theories with a nonminimal interaction between spinor and electromagnetic fields can be considered as an effective model approximately describing the spacetime foam.
The nucleon spin problem raises experimental and theoretical questions regarding the contribution of the orbital angular momentum of the quarks to the total spin of the nucleon. In this article we examine the commutation relationships of various operators that contribute to the total angular momentum of the nucleon. We find that the sum of the orbital plus gluon field angular momentum should satisfy the angular momentum commutators, at least up to the one-loop level. This requirement on the sum of these operators imposes a nontrivial restriction on the form of the color electric and magnetic fields. This is similar to the magnetic monopole/ electric charge system where it is only the sum of the orbital plus field angular momentum that satisfies the correct commutation relationships.
A wormhole with a quantum throat on the basis of an approximate model of the spacetime foam is presented. An effective spinor field is introduced for the description of the spacetime foam. The consequences of such model of the wormhole is preventing a "naked'' singularity in the Reissner-Nordström solution with $|e|/m > 1$.
It is shown that the event horizon of 4D black hole or $ds^2 = 0$ surfaces of multidimensional wormhole-like solutions reduce the amount of information necessary for determining the whole spacetime and hence satisfy the Holography principle. This leads to the fact that by matching two metrics on a $ds^2 = 0$ surface (an event horizon for 4D black holes) we can match only the metric components but not their derivatives. For example, this allows us to obtain a composite wormhole inserting a 5D wormhole-like flux tube between two Reissner-Nordström black holes and matching them on the event horizon. Using the Holography principle, the entropy of a black hole from the algorithm theory is obtained.