Der Wechselwirkungsoperator im Gitterraum

In previous papers we have developed the Dirac equation in a lattice space with a finite numberZ ³ of points. This equation is quasi relativistic. For in the limitZ→∞ we obtain the relativistic energy-momentum relation. Here we derive the quasi relativistic interaction operator from a lattice space. First we prove that, without any loss of generality, the number of particles can be assumed as constant. Then we deduce an interaction operator being uniquely defined by some postulates, the most important of which are (i) the particle-hole symmetry (either the particles or the antiparticles may be considered as holes), (ii) the Racah covariance (eigenvalues are symmetrical to zero), (iii) the Touschek covariance (eigenvalues depend only on the square of the bare massκ). The other postulates are more or less obvious: 2-particle-forces, local interaction, translation invariance and cube symmetry. In the limitZ→∞ the operator is Lorentz invariant. Since the parity symmetry is broken, some alternative systems of postulates are considered. Finally we point out that the proper elementary particles are quasi particles in a certain Dirac sea of a constant number of urfermions. Essentially as inDirac's original theory of free particles the urfermions occupy half of the quantum places of the lattice. Of course, the Dirac sea now is modified by interaction.     

Symmetrieeigenschaften achtkomponentiger Spinorfelder im Gitterraum

Starting from the four component Dirac equation for free particles without mass W.Heisenberg und W.Pauli have shown that the interaction term is uniquely defined, if one requires that all symmetries of free particles are preserved. Here we obtain similar results if we start from the eight component Dirac equation for free particles without mass:

1. The symmetry group of the eight component Dirac equation for free particles without mass has 16 parameters. It is isomorph to the direct product of the SU 4 and a one-parametric group: SU 4× (1).
2. The interaction operator is uniquely defined if one requires to preserve as many symmetries as possible of those given in (1).
3. But some of the symmetries in (1) are necessarily broken, in particular that of SU 3. The symmetry of the interaction operator is given by SO 4× (1)× (1).

These results mean:

1. The Heisenberg theory is uniquely defined, only if one assumes that the free particle part of the equation is well known.
2. The theory can be changed without modifying the fundamental idea ofHeisenberg andPauli to deduce an uniquely defined interaction operator if one starts with a modified free particle part.
3. A special kind of modification of the free particle part leads essentially to the SU 4-symmetry including that of SU 3, which is necessarily broken by the interaction term.
4. The question arises if this break of the SU 3-symmetry has something to do with the real break. This question is not yet touched in this paper.

     

Urfermionen im kubischen Gitter mit acht Punktlagen

Space is a cubic lattice of points with eight positions in each cell. — This proposition leads, in the limit of an infinite number of points and a vanishing lattice constant, to a Lorentz invariant Schrödingerian for motion if we assume, that only one kind of urfermions exists, and that transitions are possible only to next neighbours. Best adapted to the lattice is an interaction operator which is essentiallyHeisenberg's. In HF-approximation we derive the equations for the masses of quasi particles in the liquid of urfermions. In the now proposed lattice the masses are finite, if and only if the same is true for the interaction constant. We obtain the energyE=±√k ²+m ² and the massm=2.757W even in the limit. It is easy to see, why now we need only a finite value ofW.     

Zeeman-Effekt im Grundzustand von atomarem Kohlenstoff

The Landé factors of the ground state levels³ P ₁ and³ P ₂ of atomic carbon are calculated. The Hamilton operator proposed by Abragam and Van Vleck takes account of relativistic effects up to the second order. Additionally, corrections to the orbital and spin moments of the electrons are applied. The deviation from Russell-Saunders coupling is treated in perturbation theory. The results $$\begin{gathered} g_J ({}^3P_1 ) = 1.501069 \hfill \\ g_J ({}^3P_2 ) = 1.501056 \hfill \\ \end{gathered} $$ differ from the experimental values by about 10^?5.     

Zum Nachweis von änderungen im angeregten Zustand eines Atoms durch Beobachten der folgenden änderungen im Grundzustand

Radio frequency transitions in the excited state of Rb atoms are observed by measuring the transmitted light in a resonance cell experiment. The influence of additional radio frequency transitions simultaneously performed between the Zeeman sub-levels of the ground state is studied. Methods for observing signals of the excited states without using fluorescent light as detector are discussed concerning the magnetic deflection of optical oriented atoms and also the influence of recoil of the scattered light quants on the direction of an atomic beam.     

Diracgleichung im Gitterraum als Beispiel einer aus Elementarprozessen folgenden Theorie

We consider the quantum theory of particles in a lattice space with a finite number of points. Assuming a simple cube translation lattice, the Hamiltonian (Schrödingerian) for free motions is defined by the following conditions:

1. i
   The Hamiltonian for free motions is a bilinear Hermitean form ofψ ^?,ψ.     
   
   

Quasirelativistische Urfermionen

In recent papers we have reformulated the quantum theory of fermions in a lattice space with a finite number of points, sayZ ³. Of course, Lorentz invariance holds only in the limitZ→∞. So far a lattice space withZ ³ points provides us only with a convenient method to define the order of some limiting processes. — Here we discuss a more fundamental question. According to general relativity Lorentz invariance can not hold all over the world and must also be broken at tiny distances of the centers of particles. If the space curvature is not essential for the theory of elementary particles, as generally is assumed, we must only take into account the topological structure of the deviations from Lorentz invariance. In this respect the lattice space provides us with a rather rough but sufficient picture of a space, being approximately Lorentz invariant only for intermediate distances. — In a lattice withZ ³ points the Hilbert space has a finite number of dimensions. It seems to us important that this assumption will hold, even if we proceed to a more refined space model.     

Elektronenterme von Kristallen bei nichttotalsymmetrischem Grundzustand der Gitterteilchen

The splitting ofBethe's crystal levels by the interaction between the electrons of equivalent lattice particles is discussed the ground-state ofBethe's levels being degenerated. A structured spectrum may be found for mixed crystals only regarding single foreign ions and pairs of foreign ions being next neighbours. A method is given to get the energy levels of pairs fromBethe's levels by means of group theory.     

Relaxationserscheinungen im 63 P 2-Zustand des Quecksilber-Isotops199Hg bei Stößen mit Quecksilberatomen im Grundzustand

The decay ofrf resonance signals (Δm _F =± 1, ΔF=0) in the hfs-states (F=3/2, 5/2) of the 6³ P ₂-state of¹⁹⁹Hg has been observed by means of a sampling method. By comparing the relaxation times to those of the even isotopes, the cross section σ₂(F) for the destruction of an alignment in the hfs-states by collisions with ground state Hg-atoms could be measured. The following ratios were obtained: σ₂(F=3/2)/σ₂=1.04±0.06 and σ₂(F=5/2)/σ₂=0.90± 0.03. The cross section σ₂ for the even isotopes was found to be (2.620±0.265) 10^?14cm². Assuming total decoupling of nuclear spinI and electronic angular momentumJ during the collision, the cross sections for the destruction of an orientation (σ₁) and an “octupolarisation” (σ₃) could be calculated. For the even isotopes the following ratios were derived: σ₁/σ₂=0.76 ± 0.07 and σ₃/σ₂=1.08 ± 0.09.     

Der Einfluß der Wärmeleitung zur Kathode im elektrischen Feldbogen

For various cathode metalsKesaev has measured the arc lifetime as a function of current. RecentlyKingdon, assuming the field emission theory could not explain these experiments, suggested that the secondary electron emission produced by positive ions through a diffusion-controlled neutralization process determines the cathode mechanism. In this paper another assumption is made, based on the field emission theory: the cathode needs a minimal energy-supply for evaporation in order to maintain a higher vapourpressure and ion density near the cathode. For the mercury cathode this assumption seems to be valid. The temperature of the cathode spot and the voltage drop in front of it, for Bi, Pb, Zn, Tl, Cd, In, Sn, Cu, is not yet exactly known. Therefore the validity of the assumption made, concerning these materials can only be proved qualitatively.     

Der Elektromagnetische Aspekt der Magnetomechanischen Erscheinung in Gleich und im Monoalternant Pulsierenden Magnetfeld

The electromotive tension induced by Barkhausen discontinuities is studied. These Barkhausen discontinuities are excited by periodic mechanical stress in a d-c and a mono-alternating pulse magnetic field.     

Der Vordurchschlagsstrom im Hochvakuum. II. Über die Natur der Emissionszentren

Pre-breakdown currents of low order of magnitude (10⁻¹⁵–10⁻¹¹ A) were measured with UHV-conditions in order to obtain information about the nature of the emitting sites. Heating the cathode to temperatures > 600°C or ionic bombardment in a glow discharge reduced strongly the current, but it was considerably increased by oxidation. Exposure to atmospheric air and following bake-out at 400°C had a similar effect as the artificial oxidation. Hence, starting the experiments the first emission may come from nonmetallic structures as oxide needles. It is therefore concluded that special precautions are necessary in order to avoid non-metallic emission sites of high emissivity even with UHV-conditions.