Disjoining pressure of discrete surface charges on thin aqueous films

The disjoining pressure of charged parallel interfaces confining an electrolyte solution is to a large extent determined by the screening clouds of the surface charges. We evaluate the pressure in terms of the number density sigma of discrete charges and film thickness d and find, at sigmad(2) approximately 1, a crossover from the well-known law P approximately sigma(2) to a linear behavior P approximately sigma. For the latter case, each surface charge results in strongly inhomogeneous pressure profiles at both interfaces.     

Deflection of sputtered ions by surface charges

The trajectories of ions sputtered from an insulating surface carrying a surface charge have been computed. The results show that yields measured in particular directions can be in serious error as the trajectories of low energy sputtered ions depend critically on surface charge and point of origin of the ion. The distorted yield curves for 1.2 eV ions and 10 eV ions leaving a surface with a ten volt surface potential are calculated.     

The Poisson algebra of the invariant charges of the Nambu-Goto theory: Casimir elements

The reparametrization invariant non-local conserved charges of the Nambu-Goto theory form an algebra under Poisson bracket operation. The center of the formal closure of this algebra is determined. The relation of the central elements to the constraints of the Nambu-Goto theory is clarified.On leave of absence from Physics Faculty, University of Freiburg, Federal Republic of GermanyThis work was supported by Stiftung Volkswagenwerk, Deutsche Forschungsgemeinschaft and by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract De-AC03-76SF0098     

On the renormalization of the quantum field theory of point-like monopoles and charges

The quantum field theory of point-like monopoles and charges is first formulated on a euclidean lattice for a convenient regularization. The regularization preserves the peculiar features of the theory, namely those related to the invariance and to the quantization condition. The partition function is expressed as a path integral over the particle's closed paths and the action is constructed in terms of arbitrary surfaces having those paths as boundaries. The possible divergences of the continuum limit are discussed, in particular the vacuum polarization ones. It is found that, although both the electric charge Q and the magnetic charge G are renormalized as Q = Z_QQ_R and G = Z_GG_R, the quantization condition is preserved by the renormalization i.e. Z_QZ_G = 1 so that QG = Q_RG_R = 2πn. Due to the dual symmetry of the theory, then, for Q = G we get Z_Q = Z_G = 1.     

A new proposal for the determination of the renormalization group trajectories by the Monte Carlo renormalization group method

We present a new method for calculating block renormalized couplings by Monte Carlo renormalization group. This method has several advantages with respect to the existing ones and can be applied for any value of the coupling constants. A preliminary numerical study of the 2-dimensional O(3) non linear σ-model is also presented.     

Schwinger's method for the fermionic Casimir effect

The Casimir energy of a massive Dirac field confined between two parallel infinite plates is computed using a method proposed by Schwinger. The massless case is obtained as a limit of the massive case. The boundary conditions are those of zero current through the plates, as inspired by quark confinement in the MIT bag model for hadrons. We use an analytical continuation method of regularization which allows the employment of Epstein function techniques. The calculation using Schwinger's original regularization by a cutoff in proper time is also outlined.     

Influence of surface electronic structure on the Casimir force

Recent nonlocal microscopic theory of Casimir force which expresses the interaction energy between two metallic slabs in terms of surface polariton propagators calculated from diamagnetic and paramagnetic current-current response functions, sensitive to details of the surface electron density profiles and single-particle excitations on the surfaces, is used here to calculate various contributions to the Casimir energies for a silver film described by two different models. Current-current response functions are constructed from energy levels and wave functions obtained in two different models: jellium and Chulkov one-dimensional model potential, and the results are compared with the local plasmon model results. The results show how the details of such surface electronic structure modify Casimir force.     

Schwinger's method for the massive Casimir effect

We apply a method recently proposed by Schwinger to the massive scalar field to calculate the Casimir effect. The method is applied with two different regularization schemes: Schwinger's original one by means of Poisson formula and another one by means of analytical continuation.     

An efficient renormalization group improved implementation of the MSSM effective potential

In the context of MSSM, a novel improving procedure based on the renormalization group equation is applied to the effective potential in the Higgs sector. We focus on the one-loop radiative corrections computed in Landau gauge by using the mass independent renormalization scheme . Thanks to the decoupling theorem, the well-known multimass scale problem is circumvented by switching to a new effective field theory every time a new particle threshold is encountered. We find that, for any field configuration, there is a convenient renormalization scale at which the loop expansion respects the perturbation series hierarchy and the theory retains the vital property of stability. Received: 31 August 1999 / Revised version: 22 March 2000 / Published online: 23 October 2000     

On Schwinger's method for obtaining the Casimir effect

We show that a slight modification in Schwinger's method leads directly to the finite result for the Casimir energy of a massless scalar theory.     

Generation of surface plasmons in a conductor by moving charges

The surface polarization fields generated by a charge moving near a sphere or cylinder have been considered. This problem is related to the phenomena arising in an arc discharge in a gas near a solid surface during the formation of conducting cylindrical or spherical nanostructures, in particular, carbon nanotubes or fullerenes. The polarization fields, forces, energy losses, and other characteristics have been calculated.     

Lectures on the functional renormalization group method

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained by a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scaler theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.     

Casimir force pressure on the insulating layer in metal-insulator-semiconductor structures

The Casimir force pressure on the insulating layer in metal-insulator-semiconductor structures with parameters close to those used in the production of semiconductor devices has been calculated. It has been shown that the Casimir force pressure increases tenfold and reaches several tens of pascals as the insulator thickness decreases from 80 to 40 nm. The metal layer thickness and the presence of the surface layer with a high charge carrier concentration in the semiconductor have a slight effect on calculated values of the Casimir pressure.     

Charge renormalization in quantum field theory by the unitary clothing transformation method

The clothing procedure in several lowest orders in the coupling constant has been implemented using the unitary clothing transformation method. Within a simple field theory model, including interaction of charged spinless nucleons and scalar mesons, an expression for the charge shift is obtained, which is determined by the operators beyond the energy shell.     

Modulation of the Casimir force by laser pulses: Influence of oxide films on the silicon surface

The possibility of modulating the Casimir force that acts in an air medium between a gold sphere and a silicon plate irradiated by laser pulses has been studied. It has been demonstrated that the oxide film that is formed on the silicon surface in air hardly affects the possibility of modulating the Casimir force when the distances between interacting bodies are of the order of 100 nm. With an increase in the distance, the modulation depth decreases; however, this region is of less practical interest, because the Casimir forces become too weak.     

Exponents for the excluded volume problem as derived by the dynamic renormalization group method

By regarding the contour length L of a polymer chain as “time”, we derive the mean-square end-to-end distance 〈x²〉 for the polymer chain with excluded volume by means of the dynamic renormalization group. The result to first order in ? = 4 ? d (d is the dimension of the space) is $\text{〈x}{}^2\text{〉 =}\text{const}\text{× L}{}^{\mathrm{<mtext>1+?</mtext><mtext>8</mtext>}}$.     

Schwinger's method for the fermionic Casimir effect at finite temperature

The Casimir energy of a massive Dirac field at finite temperature and confined between two parallel infinite plates is computed using a method proposed by Schwinger. The boundary conditions are those of zero current through the plates, as inspired by quark confinement in the MIT bag model for hadrons. We use Schwinger's original regularization by a cutoff in proper-time. We comment on the analytical continuation method of regularization, which allows the employment of Epstein function techniques, and on the different possible expressions for the final answer.     

Radiative corrections to the Casimir pressure under the influence of temperature and external fields

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 secondorder perturbation theory at finite temperature. Thereby it turns out that the calculation of the vacuum energy at the vanishing temperature via the Z functional is much simpler than a calculation via the energy momentum tensor. This observation allows determination of the influence of static electromagnetic fields on the Casimir problem.