A possible unification of Newton's and Coulomb's forces

We have considered electric charge as the fourth component of the particle momentum in five-dimensional space–time. The fifth dimension has been compactified on a circle with an extremely small radius determined from the fundamental physics constants. First, we have given equations in the framework of five-dimensional special relativity and determined the corresponding reduction to four-dimensional space–time. Then, in order to obtain an appropriate charge-to-mass ratio and to avoid the Fourier modes problem, we have considered the propagation of an off-mass shell particle in the five-dimensional space–time which can be interpreted as the motion of an on-mass shell particle in the four-dimensional world we experience. As an example, we have discussed the five-dimensional kinematic equations associated with the electron-positron annihilation process into two photons. Finally, the consequences on the gravitational interaction between two elementary charged particles has been studied. As a main result, we have obtained a unification of Newton's gravitational and Coulomb's electrostatic forces.     

Hydrogenic atom multiphonon ionization by intense fields with green's method

An expression for n-photon cross-section ionization of hydrogenic atoms by intense linearly polarized light is obtained using the second quantification formalism for the radiation and the Green's function method. It is shown that it reduces into Stobbe's formula in the one photon case.     

The Miura transformations of Kaup's equation and of Mikhailov's equation

Two types of Miura transformations have been found. One relates Kaup's equation to Sawada-Kotera's equation and another relates the generalized Mikhailov equation to a model equation for a shallow water wave.     

Breakdown of Kohler's rule in Indium at low temperatures

Precise measurements of the transverse magnetoresistivity of pure samples of Indium between 3.4° and 7.8°K show that Kohler's rule is not strictly valid. Deviations from Kohler's rule occur even when the analysis is restricted to data obtained for a single sample in small magnetic fields.     

Goldstone modes on Wilson's surface

In three-dimensional compact QED in its continuum formulation, Goldstone modes associated with surface fluctuations cause Wilson's surface to wander infinitely far from the minimal surface. On the lattice, this is only true for small coupling, due to the roughening transition.     

Freundlich's adsorption isotherm

We present a brief derivation of Freundlich's adsorption isotherm using straightforeward methods of statistical mechanics. The assumption that the adsorbed atoms move in Morse potential wells of different depths leads to the observed compensation effect in the energy dependence of the occupation probability of surface sites, essential for the understanding of Halsey's form of the Freundlich isotherm.     

MacDonald's theorem and Milatz's theorem for multivariate stochastic processes

MacDonald's theorem, which expresses the spectral density of a randomly fluctuating variable α(t) in terms of the finite time average of that variable, α_θ(t), is generalized for multivariate processes. For purely random processes, having a white spectrum, this also yields the corresponding generalization of Milatz's theorem.     

Canonical quantization of the electromagnetic field with Dirac's monopoles

From a lagrangian theory of charge-monopole electrodynamics which uses strings but is free from Dirac's veto, a hamiltonian theory is derived which describes the interaction between electric and magnetic point particles and photons.     

On the relation of two approaches to Rubin's model of brownian particles

The relation between two approaches to Rubin's model of brownian particles is clarified. The Fokker-Planck-like equation for the model is thereby derived.     

Ambiguity of the equivalence principle and Hawking's temperature

There are two inequivalent ways in which the laws of physics in a gravitational field can be related to the laws in an inertial frame, when quantum mechanical effects are taken into account. This leads to an ambiguity in the derivation of Hawking's radiation temperature for a black hole: it could be twice the value usually considered.     

Dirac's extended electron model

Dirac's extended electron model is elaborated here both on the classical and quantum level. The classical equations of motion are deduced from Dirac's action principle. It is shown that the model is free of the troublesome runaway solutions in the classical theory. The quantum theory of the radial oscillations is worked out in detail and the spectrum is discussed. The stability of the model is studied and it is found that Dirac's extended electron is unstable against quadrupole deformations.     

Relation between generalized idempotency of Dirac's density operator and semigroup property of Bloch's density operator

It is shown that a generalized form of idempotency of Dirac's density operator is a necessary and sufficient condition for semigroup property of Bloch's density operator.     

Extending Kraitchman's equations

Kraitchman's method for the determination of the substitution (or r_s) coordinates of an atom in a rotating molecule (asymmetric rotor) from the two sets of three principal moments of inertia of the common isotope of the molecule and the species where the particular atom has been isotopically substituted, has been extended to include the complete coordinate transformation between the principal axis systems of both molecular species. No additional information is required. Several applications are discussed, including a method which helps solve the problem of “small coordinates” by following an appropriate “substitution sequence.”     

Green's functions for gravitational multi-instantons

The Green's functions for scalar fields propagating on the self-dual gravitational multi-instantons and multi-Taub-NUT metrics are given explicitly in closed form. The special cases for flat space, Taub-NUT and the Eguchi-Hanson instanton are listed. A construction is described for obtaining the Green's functions for fields of arbitrary spin.     

A note on Keldysh's perturbation formalism

The expansion theorem of quantum field theoy relating Heisenberg operators to asymptotic free-field operators is rewritten by means of the time-path technique, originally due to Schwinger, which to date has only found application in statistical mechanics. The theorem is combined with Bogoliubov's initial condition of vanishing correlations in the infinite past to rederive Keldysh's perturbation scheme for non-equilibrium statistical Green's functions.     

Teller's conditions regained

Recent criticism againts Teller's conditions for the crossing of potential energycurves is shown to be unjustified.     

Slavnov-Taylor identities in Weinberg's renormalization scheme

Weinberg's renormalization scheme, although more cumbersome from the computational point of view, has a more immediate physical interpretation than 't Hooft's minimal renormalization scheme. It is expected to lead to smaller higher-order coefficients in a perturbative approach to QCD. However, it a priori violates the Slavnov-Taylor identities. A complete study of this problem is performed, both theoretically and for the practitioner's sake. The ambiguities in the choice of the tensorial basis of some of the QCD vertices, as well as the dependence in the gauge parameter are used for substantiating, eventually, the Slavnov-Taylor identities in this renormalization scheme.     

Weyl's association,Wigner's function and affine geometry

According to Weyl one may associate a function with a dynamical operator; these functions depend on the parameters p and q and can be displayed in a p, q manifold, the W space. In the classical limit the W space becomes the phase space parametrised by the canonical variables. The function associated in this manner with the density operator is Wigner's function. It turns out that if Wigner's function is a delta function it cannot represent the density operator of a physically realisable state unless the argument of the delta-function is linear in the parameters a and q. In all other cases Wigner's function associated with a physically realisable state has a finite width, proportional to $\text{h}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$. Consequently straightness (linear combination of p and q) has a fundamental significance in the W space. Since this property is preserved under linear inhomogeneous transformations the W space will have a geometry generated by these transformations, the affine geometry of Euler, Moebius and Blaschke. In the present note we show how this comes about, how it simplifies the semiclassical approximations of Wigner's function, and makes one understand how in the classical limit this geometry is lost, allowing to be replaced by the geometry of canonical transformations.     

Nonlinear superposition rule for Abel's equation

A nonlinear superposition rule for Abel's cubic differential equation involving four particular solutions can be replaced by a superposition rule involving only two particular solutions. Chiellini's restrictions on the particular solutions are found to be satisfied.     

The bound particle spatial density distribution in Appelbaum-Kondo's trial ground state of Kondo's Hamiltonian

In view of incomplete treatments the charge (spin) density of the bound particle in Appelbaum-Kondo's trial ground state of Kondo's Hamiltonian is recalculated. The asymptotic behaviour at large distances from the impurity is at variance with earlier findings.