the main task of drilling the formation by the bit is done via scraping, crushing and grinding. discharging the fluid from the bit nozzles is done with high pressure which assists to break the rocks. different parameters affect the bit selection and design for each drilling formation, but the most important one is drillability that depends on hardness of the formation. in this paper, the design...

In order to get a clue to understanding the volume-dependence of vortex free energy (which is defined as the ratio of the twisted against the untwisted partition function), we investigate the relation between vortex free energies defined on lattices of different sizes. An equality is derived through a simple calculation which equates a general linear combination of vortex free energies defined ...

The new method of nonperturbative calculation of the beta-function in the lattice gauge theory is proposed. The method is based on the finite size scaling hypothesis. Ever since the pioneering work by Creutz [1] the approach to asymptotic scaling, and thus the continuum limit, was one of the central issues in studies of gauge theories on the lattice. Although the first results were promising, t...

Using the higher covariant derivatives regularization of gauge theories in the framework of the background field method, supplemented with one-loop Pauli-Villars regulator fields, we obtain a version of the renormalization group equation for the regulator fields, whose vacuum energy depends on the background gauge field. It is evaluated using an anomalous Ward-Takahashi identity, which is relat...

Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as well as about a reference frame in which this geometry is studied. We consider the evolution of a physical object (the Universe) in “physical” subspace of ex...

We derive the master function governing the component action of the four-dimensional non-anticommutative (NAC) and fully N=2 supersymmetric gauge field theory with a non-simple gauge group U(2) = SU(2) × U(1). We use a Lorentz-singlet NACdeformation parameter and an N=2 supersymmetric star (Moyal) product, which do not break any of the fundamental symmetries of the undeformed N=2 gauge theory. ...

We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynamical symmetry breaking, in the light of its Landau-Khalatnikov-Fradkin transformation (LKFT). In the former case, starting with the massive bare propagator in the Landau gauge, we obtain non perturbative propagator in an arbitrary covariant gauge. Carrying out a perturbative expansion of this result,...

We consider a U(1) gauge theory, minimally coupled to a massless Dirac field, where a higher-derivative term is added to the pure gauge sector, as in the Lee-Wick models. We find that this term can trigger chiral symmetry breaking at low energy in the weak coupling regime. Then, the fermion field acquires a mass that turns out to be a function of both the energy scale associated to the higher-d...

We address in a recent gauge model of unparticles the issues that are important for consistency of a gauge theory, i.e., unitarity and Ward identity of physical amplitudes. We find that non-integrable singularities arise in physical quantities like cross section and decay rate from gauge interactions of unparticles. We also show that Ward identity is violated due to the lack of a dispersion rel...

We derive the master function governing the component action of the four-dimensional non-anticommutative (NAC) and fully N=2 supersymmetric gauge field theory with a non-simple gauge group U(2) = SU(2) × U(1). We use a Lorentz-singlet NACdeformation parameter and an N=2 supersymmetric star (Moyal) product, which do not break any of the fundamental symmetries of the undeformed N=2 gauge theory. ...