D. Robaschik

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

Quantum field theoretic treatment of the Casimir effect

\alpha

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

-representation of Greens functions.

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

A nontrivial quantum field theoretical treatment of the Casimir effect demands the quantization of spinor electrodynamics with boundary conditions. The boundary conditions are realized by two super conducting infinitely thin parallel plates. As a technical tool we use the path integral method. It is shown that in perturbation theoretical calculations the standard Feynman rules remain valid up to a modification of the photon propagator. One advantage of our procedure is the derivation of a closed expression for this modified photon propagator in a covariant gauge which allows the explicit calculation of loop diagrams. Up to the order e2 we determine the radiative correction for vacuum energy density expression and the Casimir force. It turns out that the distance dependent part of the energy density and thereby the Casimir force is ultraviolet finite. An explicit value is obtained in the limit of large distances (in comparison with the Compton wave length).

Vacuum energy in quantum field theory with external potentials concentrated on planes

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.

Radiative Corrections to the Casimir Pressure Under the Influence of Temperature and External Fields

Abstract The non-singlet and singlet evolution kernels of the twist-2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in ¢O(α s ) for the general case of virtualities q2, q′2 ≠ 0. Special cases as the kernels for the general single-variable evolution equation and the Altarelli-Parisi and Brodsky-Lepage limits are derived from these results.

Light-cone expansion in renormalized perturbation theory

In the presence of an idealized potential on two parallel planes represented by two one-dimensional delta -functions at x3=-d/2 and x3=+d/2 the authors discuss the Feynmann propagators for relativistic scalar and spinor fields. These propagators take into account bound states, scattering states and resonances. The Casimir energy for this configuration is calculated. For massive fields the Casimir force decreases exponentially with rising distances. In the scalar case they find an attractive force and in the spinor case a repulsive force. An attempt to treat the same problem for a massive scalar field using nonrelativistic quantum field theory leads to a vanishing Casimir force.

Target mass corrections for virtual Compton scattering at twist-2 and generalized, nonforward Wandzura–Wilczek and Callan–Gross relations

Generalizing the quantum field theory (QFT) with boundary conditions in covariant gauge to the case of finite temperature, we develop the quantum electrodynamics (QED) with boundary conditions in the Matsubara approach as well as in the thermofield formulation. We rederive the known results of the free-field theory for the pressure and the free energy of the Casimir problem. For infinitely thin plates we calculate the radiative corrections in second-order perturbation theory at finite temperature. Thereby it turns out that the calculation in of the vacuum energy at the vanishing temperature via the Z functional is much simplier than the calculation via the energy momentum tensor. This observation allows determination of the influence of static electromagnetic fields on the Casimir problem. copyright 1987 Academic Press, Inc.

Scaling violations of diffractive structure functions: operator approach

Abstract The existence of the light-cone expansion in renormalized perturbation theory is proved. The proof relies in an essential way on the method of Anikin and Zavialov which applies new subtraction operators and allows the elimination of a remainder which is small for x 2 →0. It is shown that the light-cone expansion converges weakly on a dense subset of the Fock space to the difference between the operator product and a remainder.

Power corrections of off-forward quark distributions and harmonic operators with definite geometric twist

Abstract The off-cone Compton operator of twist-2 is Fourier transformed using a general procedure which is applicable, in principle, to any QCD tensor operator of definite (geometric) twist. That method allows, after taking the nonforward matrix elements, to separate quite effectively their imaginary part and to reveal some hidden structure in terms of appropriately defined variables, including generalized Nachtmann variables. In this way, without using the equations of motion, generalizations of the Wandzura–Wilczek relation and of the mass-corrected Callan–Gross relation to the nonforward scattering, having the same shape as in the forward case, are obtained. In addition, new relations for those structure functions which vanish in the forward case are derived. All the structure functions are expressed in terms of iterated generalized parton distributions of nth order. In addition, we showed that the absorptive part of twist-2 virtual Compton amplitude is determined by the nonforward extensions of g 1 , W 1 and W 2 only.