B. Geyer

Wave functions, evolution equations and evolution kernels from light ray operators of QCD

The widely used nonperturbative wave functions and distribution functions of QCD are determined as matrix elements of light-ray operators. These operators appear as large momentum limit of nonlocal hadron operators or as summed up local operators in light-cone expansions. Nonforward one-particle matrix elements of such operators lead to new distribution amplitudes describing both hadrons simultaneously. These distribution functions depend besides other variables on two scaling variables. They are applied for the description of exclusive virtual Compton scattering in the Bjorken region near forward direction and the two meson production process. The evolution equations for these distribution amplitudes are derived on the basis of the renormalization group equation of the considered operators. This includes that also the evolution kernels follow from the anomalous dimensions of these operators. Relations between different evolution kernels (especially the Altarelli-Parisi and the Brodsky-Lepage) kernels are derived and explicitly checked for the existing two-loop calculations of QCD. Technical basis of these results are support and analytically properties of the anomalous dimensions of light-ray operators obtained with the help of the

Zeta function determinant of the Laplace operator on the D-dimensional ball

\alpha

The Altarelli-Parisi kernel as asymptotic limit of an extended Brodsky-Lepage kernel

-representation of Greens functions.

Casimir force at both nonzero temperature and finite conductivity

We present a direct approach for the calculation of functional determinants of the Laplace operator on balls. Dirichlet and Robin boundary conditions are considered. Using this approach, formulas for any value of the dimension,D, of the ball, can be obtained quite easily. Explicit results are presented here for dimensionsD=2,3,4,5 and 6.

Constraints for hypothetical interactions from a recent demonstration of the Casimir force and some possible improvements

Abstract An extended flavour non-singlet Brodsky-Lepage kernel is defined as the anomalous dimension of a light-ray operator. Introducing a new distribution function containing the Altarelli-Parisi quark distribution function as a special case we obtain a new set of evolution equations which induce a relation between the AP- and the extended BL-kernels. Thereby the consistency of the existing two-loop results is confirmed.

The virtual Compton amplitude in the generalized Bjorken region: Twist-2 contributions

We find the combined effect of nonzero temperature and finite conductivity onto the Casimir force between real metals. Configurations of two parallel plates and a sphere (lens) above a plate are considered. Perturbation theory in two parameters (the relative temperature and the relative penetration depth of zero-point oscillations into the metal) is developed. Perturbative results are compared with computations. Recent improper computations based on the Lifshitz formula for the temperature Casimir force are discussed.

Lifshitz-type formulas for graphene and single-wall carbon nanotubes: van der Waals and Casimir interactions

The Casimir force is calculated in the configuration of a spherical lens and a disc of finite radius covered by Cu and Au thin layers which was used in a recent experiment. The correction to the Casimir force due to finiteness of the disc radius is shown to be negligible. Also the corrections are discussed due to the finite conductivity, large-scale and short-scale deviations from the perfect shape of the bounding surfaces and the temperature correction. They were found to be essential when confronting the theoretical results with experimental data. Both Yukawa-type and power-law hypothetical forces are computed which may act in the configuration under consideration due to the exchange of light and/or massless elementary particles between the atoms of the lens and the disc. New constraints on the constants of these forces are determined which follow from the fact that they were not observed within the limits of experimental errors. For Yukawa-type forces the new constraints are up to 30 times stronger than the best ones known today. A possible improvement of experimental parameters is proposed which gives the possibility to strengthen constraints on Yukawa-type interactions up to

Evolution kernels of twist 2 light-ray operators for unpolarized and polarized deep inelastic scattering

{10}^{4}

Leading logarithmic evolution of the off-forward distributions

times and on power-law interactions up to several hundred times.

Surface-impedance approach solves problems with the thermal Casimir force between real metals

Abstract A systematic derivation is presented of the twist-2 anomalous dimensions of the general quark and gluon light-ray operators in the generalized Bjorken region in leading order both for unpolarized and polarized scattering. Various representations of the anomalous dimensions are derived in the non-local and local light cone expansion and their properties are discussed in detail. Evolution equations for these operators are derived using different representations. General two- and single-variable evolution equations are presented for the expectation values of these operators for non-forward scattering. The Compton amplitude is calculated in terms of these distribution amplitudes. In the limit of forward scattering a new derivation of the integral relations between the twist-2 contributions to the structure functions is given. Special limiting cases which are derived from the general relations are discussed, as the forward case, near-forward scattering, and vacuum-meson transition. Solutions of the two-variable evolution equations for non-forward scattering are presented.