A String Approximation for Cooper Pair in High-Tc_{\bf c} superconductivity

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.Comment: Essential changes: (a) the section is added in which it is shown that Green's function method in the superconductivity theory is a realization of discussed Heisenberg quantization method; (b) Veneziano amplitude is discussed as an approximation for the 4-point Green's function in High-T_c; (c) it is shown that Eq.(53) has more natural solution on the layer rather than on 3 dimensional spac

The actual content of quantum theoretical kinematics and mechanics

First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantum mechanics. Canonically conjugated variables are determined simultaneously only with a characteristic uncertainty. This uncertainty is the intrinsic reason for the occurrence of statistical relations in quantum mechanics. Mathematical formulation is made possible by the Dirac-Jordan theory. Beginning from the basic principles thus obtained, macroscopic processes are understood from the viewpoint of quantum mechanics. Several imaginary experiments are discussed to elucidate the theory

Two-dimensional anyons and the temperature dependence of commutator anomalies

The temperature dependence of commutator anomalies is discussed on the explicit example of particular (anyonic) field operators in two dimensions. The correlation functions obtained show that effects of the non-zero temperature might manifest themselves not only globally but also locally.Comment: 11 pages, LaTe

Entanglement condition via su(2) and su(1,1) algebra using Schr{\"o}dinger-Robertson uncertainty relation

The Schr{\"o}dinger-Robertson inequality generally provides a stronger bound on the product of uncertainties for two noncommuting observables than the Heisenberg uncertainty relation, and as such, it can yield a stricter separability condition in conjunction with partial transposition. In this paper, using the Schr{\"o}dinger-Robertson uncertainty relation, the separability condition previously derived from the su(2) and the su(1,1) algebra is made stricter and refined to a form invariant with respect to local phase shifts. Furthermore, a linear optical scheme is proposed to test this invariant separability condition.Comment: published version, 3.5 pages, 1 figur

Dynamical F(R)F(R) gravities

It is offered that $F(R)-$modified gravities can be considered as nonperturbative quantum effects arising from Einstein gravity. It is assumed that nonperturbative quantum effects gives rise to the fact that the connection becomes incompatible with the metric, the metric factors and the square of the connection in Einstein - Hilbert Lagrangian have nonperturbative additions. In the simplest approximation both additions can be considered as functions of one scalar field. The scalar field can be excluded from the Lagrangian obtaining $F(R)-$gravity. The essence of quantum correction to the affine connection as a torsion is discussed.Comment: discussion on quantum corrections is adde

Spherically Symmetric Solution for Torsion and the Dirac equation in 5D spacetime

Torsion in a 5D spacetime is considered. In this case gravitation is defined by the 5D metric and the torsion. It is conjectured that torsion is connected with a spinor field. In this case Dirac's equation becomes the nonlinear Heisenberg equation. It is shown that this equation has a discrete spectrum of solutions with each solution being regular on the whole space and having finite energy. Every solution is concentrated on the Planck region and hence we can say that torsion should play an important role in quantum gravity in the formation of bubbles of spacetime foam. On the basis of the algebraic relation between torsion and the classical spinor field in Einstein-Cartan gravity the geometrical interpretation of the spinor field is considered as ``the square root'' of torsion.Comment: 7 pages, REVTEX, essential changing of tex

Formulation of the Spinor Field in the Presence of a Minimal Length Based on the Quesne-Tkachuk Algebra

In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen. {\bf 39}, 10909, 2006) introduced a (D+1)-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian formulation of the spinor field in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where $\beta'=2\beta$ up to first order over deformation parameter $\beta$. It is shown that the modified Dirac equation which contains higher order derivative of the wave function describes two massive particles with different masses. We show that physically acceptable mass states can only exist for $\beta<\frac{1}{8m^{2}c^{2}}$. Applying the condition $\beta<\frac{1}{8m^{2}c^{2}}$ to an electron, the upper bound for the isotropic minimal length becomes about $3 \times 10^{-13}m$. This value is near to the reduced Compton wavelength of the electron $(\lambda_c = \frac{\hbar}{m_{e}c} = 3.86\times 10^{-13} m)$ and is not incompatible with the results obtained for the minimal length in previous investigations.Comment: 11 pages, no figur

On the statistical theory of turbulence

A study is made of the spectrum of isotropic turbulence with the aid of the customary method of Fourier analysis. The spectrum of the turbulent motion is derived to the smallest wave lengths, that is, into the laminar region, and correlation functions and pressure fluctuations are calculated. A comparison with experimental results is included. Finally, an attempt is made to derive the numerical value of a constant characteristic of the energy dissipation in isotropic turbulence

A method to measure vacuum birefringence at FCC-ee

It is well-known that the Heisenberg-Euler-Schwinger effective Lagrangian predicts that a vacuum with a strong static electromagnetic field turns birefringent. We propose a scheme that can be implemented at the planned FCC-ee, to measure the nonlinear effect of vacuum birefringence in electrodynamics arising from QED corrections. Our scheme employs a pulsed laser to create Compton backscattered photons off a high energy electron beam, with the FCC-ee as a particularly interesting example. These photons will pass through a strong static magnetic field, which changes the state of polarization of the radiation - an effect proportional to the photon energy. This change will be measured by the use of an aligned single-crystal, where a large difference in the pair production cross-sections can be achieved. In the proposed experimental setup the birefringence effect gives rise to a difference in the number of pairs created in the analyzing crystal, stemming from the fact that the initial laser light has a varying state of polarization, achieved with a rotating quarter wave plate. Evidence for the vacuum birefringent effect will be seen as a distinct peak in the Fourier transform spectrum of the pair-production rate signal. This tell-tale signal can be significantly above background with only few hours of measurement, in particular at high energies.Comment: Presented by UIU at the International Symposium on "New Horizons in Fundamental Physics: From Neutrons Nuclei via Superheavy Elements and Supercritical Fields to Neutron Stars and Cosmic Rays," held to honor Walter Greiner on his 80th birthday at Makutsi Safari Farm, South Africa, November 23-29, 201