Mφller Energy-Momentum Complex in General Relativity for Higher Dimensional Universes

Using the Mφ11er energy-momentum definition in general relativity （GR） we calculate the total energy-momentum distribution associated with （n 4- 2）-dimensional homogeneous and isotropic model of the universe. It is found that total energy of M~ller is vanishing in （n 4- 2） dimensions everywhere but n-momentum components of Mφ11er in （n 4- 2） dimensions are different from zero. Also, we evaluate the static Einstein Universe, FRW universe and de Sitter universe in four dimensions by using （n 4- 2）-type metric, then calculate the Mφ11er energy-momentum distribution of these spacetimes. However, our results are consistent with the results of Banerjee and Sen, Xulu, Radinschi, Vargas, Cooperstock-Israelit, A ygiin et al., Rosen, and Johri et al. in four dimensions.     

Møller was right

Direct calculation proves that the total energy-momentum vector derived from the Møller energy-momentum complex from 1958 does not transform like a free 4-vector with respect to the Lorentz transformation. This conforms with the conclusion formulated by Møller himself, but it contradicts the result of the critical analysis of Kovacs. Defects in Kovacs argumentation are found.     

One-loop chiral amplitudes of Møller scattering process

The high energy amplitudes of the large angles Møller scattering are calculated in the frame of chiral basis in Born and 1-loop QED level. Taking into account as well the contribution from emission of soft real photons the compact relations free from infrared divergences are obtained. The expressions for the contributions to the cross section of individual chiral amplitudes are in agreement with renormalization group predictions.     

Møller’s Energy-Momentum Complex for a Spacetime Geometry on a Noncommutative Curved D3-Brane

Møller’s energy-momentum complex is employed in order to determine the energy and momentum distributions for a spacetime described by a “generalized Schwarzschild” geometry in (3+1)-dimensions on a noncommutative curved D3-brane in an effective, open bosonic string theory. The geometry considered is obtained by an effective theory of gravity coupled with a nonlinear electromagnetic field and depends only on the generalized (effective) mass and charge which incorporate corrections of first order in the noncommutativity parameter.     

One-loop approximation of Møller scattering in generalized Krein-space quantization

It has been shown that the negative-norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter spacetime. In this processes ultraviolet and infrared divergences have been automatically eliminated. A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime (λφ ⁴) has been achieved through the consideration of the negative-norm states defined in Krein space. It has been shown that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuation, results in quantum field theory without any divergences. Pursuing this approach, we express Wick’s theorem and calculate Møller scattering in the one-loop approximation in generalized Krein space. The mathematical consequence of this method is the disappearance of the ultraviolet divergence in the one-loop approximation.     

Precision measurement of the weak mixing angle in Møller scattering

We report on a precision measurement of the parity-violating asymmetry in fixed target electron-electron (M?ller) scattering: A(PV) = [-131 +/- 14(stat) +/- 10(syst)] x 10(-9), leading to the determination of the weak mixing angle sin2(thetaW(eff) = 0.2397 +/- 0.0010(stat) +/- 0.0008(syst), evaluated at Q2 = 0.026 GeV2. Combining this result with the measurements of sin2(thetaW(eff) at the Z0 pole, the running of the weak mixing angle is observed with over 6sigma significance. The measurement sets constraints on new physics effects at the TeV scale.     

Two-loop electroweak vertex corrections for polarized Møller scattering

The contributions to the electron-electron-photon vertex of two-loop electroweak corrections are calculated. The relative correction to the parity-violating asymmetry of Møller scattering for the case of 11 GeV electron scattered off the electron at rest is found to be about–0.0034 and should be taken into account at future experiment MOLLER at JLab.     

Constructing Hadamard States via an Extended Møller Operator

We consider real scalar field theories, whose dynamics is ruled by normally hyperbolic operators differing only by a smooth potential V. By means of an extension of the standard definition of Møller operator, we construct an isomorphism between the associated spaces of smooth solutions and between the associated algebras of observables. On the one hand, such isomorphism is non-canonical, since it depends on the choice of a smooth time-dependant cut-off function \({\chi}\). On the other hand, given any quasi-free Hadamard state for a theory with a given V, such isomorphism allows for the construction of another quasi-free Hadamard state for a different potential. The resulting state preserves also the invariance under the action of any isometry, whose associated Killing field \({\xi}\) is complete and fulfilling both \({\mathcal{L}_\xi V=0 \,\, {\rm and} \,\, \mathcal{L}_\xi\chi=0}\). Eventually, we discuss a sufficient condition to remove on static spacetimes, the dependence on the cutoff via a suitable adiabatic limit.     

Analytical nuclear gradients of the explicitly correlated Møller–Plesset second-order energy

The analytical computation of nuclear gradients has been derived and implemented for the explicitly correlated second-order Møller–Plesset method (MP2-F12). The implementation has been accomplished in the TURBOMOLE program package for ansatz MP2-F12/2*A. A Slater-type geminal expanded in six Gaussian geminals (STG-6G), a complementary auxiliary basis set (CABS), and robust density fitting approximations are used. In addition, a second-order perturbation theory correction for single excitations into the complementary auxiliary basis set (CABS singles) is included to reduce the Hartree–Fock error. Smooth convergence towards the basis set limit is observed for a selection of molecules. For computations on dimers of weakly interacting molecules in small basis sets, explicitly correlated second-order Møller–Plesset theory outperforms conventional second-order Møller–Plesset theory because basis set superposition errors are largely avoided at the MP2-F12/2*A level.     

Complete calculation of electroweak corrections for polarized Møller scattering at high energies

A complete calculation of electroweak radiative corrections to observables of polarized Møller scattering at high energies was performed. This calculation took explicitly into account contributions caused by hard bremsstrahlung. A FORTRAN code that permitted including radiative corrections to high-energy Møller scattering under arbitrary electron-detection conditions was written. It was shown that the electroweak corrections caused by hard bremsstrahlung were rather strongly dependent on the choice of experimental cuts and changed substantially the polarization asymmetry in the region of high energies and over a broad interval of scattering angles.     

A new class of Fermionic Projectors: Møller operators and mass oscillation properties

Recently, a new functional analytic construction of quasi-free states for a self-dual CAR algebra has been presented in Finster and Reintjes (Adv Theor Math Phys 20:1007, 2016). This method relies on the so-called strong mass oscillation property. We provide an example where this requirement is not satisfied, due to the nonvanishing trace of the solutions of the Dirac equation on the horizon of Rindler space, and we propose a modification of the construction in order to weaken this condition. Finally, a connection between the two approaches is built.     

Observation of parity nonconservation in møller scattering

We report a measurement of the parity-violating asymmetry in fixed target electron-electron (M?ller) scattering: A(PV)=[-175+/-30(stat)+/-20(syst)] x 10(-9). This first direct observation of parity nonconservation in M?ller scattering leads to a measurement of the electron's weak charge at low energy Q(e)(W)=-0.053+/-0.011. This is consistent with the standard model expectation at the current level of precision: sin((2)theta(W)(M(Z))((-)MS)=0.2293+/-0.0024(stat)+/-0.0016(syst)+/-0.0006(theory).     

Electroweak radiative corrections to polarized Møller scattering at high energies

The cross section for with arbitrary electron polarizations is calculated within the Electroweak Standard Model for energies large compared to the electron mass, including the complete virtual and soft-photonic radiative corrections. The relevant analytical results are listed, and a numerical evaluation is presented for the unpolarized and polarized cross sections as well as for polarization asymmetries. The relative weak corrections are typically of the order of 10%. At low energies, the bulk of the corrections is due to the running of the electromagnetic coupling constant. For left-handed electrons, at high energies the vertex and box corrections involving virtual W bosons become very important. The polarization asymmetry is considerably reduced by the weak radiative corrections. Received: 22 July 1998 / Published online: 8 September 1998     

A Higher Dimensional Cosmological Model in a Scale-Covariant Theory of Gravitation

Kaluza-Klein space-time is considered in the presence of a perfect fluid distribution in the scale-covariant theory of gravitation by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983), a cosmological model in five dimensions with a negative constant deceleration parameter is presented in this theory. Some physical and kinematical properties of the model are also discussed.     

Photoionisation of atoms and Möller operators

The motion of an hydrogenoïd atom in a laser field is usually given by the time-dependent hamiltonian H(t)=[p?A(t)]²/2+V(r) where V(r) is the atomic potential whileA(t) is to be connected with the laser field. The existence and unicity for the Cauchy problem of the solutions of the corresponding Schrödinger equation are established under mild conditions onA(t) and V(r). The existence of Möller operators is investigated in two cases, namely, when the laser field is a function of time only and when it vanishes asymptotically in time. Special attention is paid for the Coulomb case for which a “distorted” Möller operator is derived. Finally, when the laser field vanishes ast→∞, the photoionisation probability is properly defined by means of the Möller operator $$\Omega (H_{At} ,H) = s - \mathop {\lim }\limits_{t \to \infty } U_{At} (t)^{ - 1} U(t)$$ , whereU(t) is the evolution operator for the system whileU _Att (t) is the evolution operator for the atom.     

Density Distribution of Bose Condensed Gas in a Three—Dimensional Optical Lattice

For the Bose-condensed gas in a magnetic trap and three-dimensional optical lattice,the non-unifrom distribution of the atoms in different lattice sited in investigated and a propagatro method is used to study the evolution of the interference pattern after the combined potentials are switched off.The analytical result of the wavefunction at any time t is given and especially the motion of the side peaks is described by a simple analytical expression.     

Bhabha versus Møller scattering as a contact-interaction analyzer at a polarized Linear Collider

We discuss electron-electron contact-interaction searches in the processes and at planned Linear Colliders run in the e ⁺ e ^- and e ^- e ^- modes with both beams longitudinally polarized. Our analysis is based on the measurement, for the two processes, of polarized differential cross sections, and allows one to simultaneously take into account the general set of electron contact-interaction couplings as independent, non-zero, parameters thus avoiding the simplifying choice of a model. We evaluate the corresponding model-independent constraints on the contact coupling constants, emphasizing the role of the available beam polarization and the complementarity, as far as the chirality of the constants is concerned, of the two processes in giving the best constraints. Received: 15 October 2002, Revised: 28 April 2003, Published online: 18 June 2003