On the geometric structure of a parity-conserving relativistic quantum field theory

Wheeler's conjecture that there might exist a ‘principle’ which rules out parity-non-conserving spaces is analysed. The following result has been obtained: A local relativistic quantum field theory is parity-conserving if the following conditions hold:

1. The fields are derived from geometry, i.e. they are represented by quantised currents (in the sense of de Rham); and
2. The theory may be defined on a connected and, under certain restrictions, on a disconnected orientable space-time continuumM ⁴.

     

Neutrinos in general relativity: Four(?) levels of approach

The three subsequent levels of approach to the problem of the neutrino in general relativity which have been exploited till now, are:

1. ‘classical particle’ approach, i.e. a study on the neutrino as a classical particle in a classical, given gravitational field;
2. ‘quantum particle’ approach, i.e. considering the Dirac equation for the neutrino in a given gravitational field;
3. ‘classical field’ approach comprising the study of combined neutrino-gravitational fields.

Many results obtained along these lines are presented, with emphasis upon the geometrical theory of two-component neutrino-gravitational fields. A synthesis of the particle and fields aspects of the neutrino could provide a possible fourth, till now non-existing, ‘quantum field’ level of approach. This should deal with a guantized neutrino field in a curved space-time (which might be also quantized, but perhaps this should belong already to a next, fifth level of approach). Studies on the neutrino physics in gravitational fields reveal not only a series of results which are of interest in se, and which may be used as the basis to a unified theory of neutrino and gravitational fields (the Rainich problem for the neutrino). They provide in addition the necessary material for astrophysical and cosmological applications; some of these are outlined in relation to the results presented.     

The moment of inertia at the saddle point of low energy fission of even-even nuclei

We use the molecular model of low energy fission, which describes the nucleus by two interacting fragments, to calculate the moment of inertia for U²³⁶ in the cranking approximation including BCS theory. We show that the moment of inertia at the saddle point:

1. depends almost linearly on the fragment distance.
2. is influenced only very weakly by the pairing constant and by the fragment deformations.
3. shows, as a function of the distribution of mass between the two fragments (A ₁ ,A ₂ ), a minimum near the magic configurationA ₁=132,Z ₁=50 and depends in this mass region strongly on the term structure near the Fermi energy.
4. is approximately that of a rigid body.

     

Testing general relativity: Progress,problems, and prospects

Recent results from radar and radio gravity experiments are:

1. Retardation of radar signals: 1.02 +?0.05 (planetary radar), 1.00 +? 0.04 (spacecraft);
2. Deflection of radio waves: 0.99 +? 0.12 (short baseline interferometry), +0.15 1.04 (short baseline interferometry), ?0.10. 0.90 +? 0.05 (short baseline interferometry);
3. Relativistic perihelion advance of Mercury: 0.99 +? 0.03 (planetary radar), 1.00 +? 0.01 (radar plus optical);
4. Time variation of the gravitational constant: (G/G) < 4 ×10^?10/yr (planetary radar). The first three results are expressed as fractions of the corresponding effects predicted by general relativity. In terms of the Eddington-Robertson parameters, the first two are approximately equal to (1+γ)/2 and the third to (2 + 2γ-β)/3. The third result depends on the assumption that the solar gravitational quadrupole moment vanishes; its effects cannot be separated usefully from those of general relativity with the present data set. The uncertainties are as given by the individual experimenters; in some cases they represent formal standard errors, in others an allowance for possible systematic errors is included.

     

Absence of singular continuous spectrum for certain self-adjoint operators

We give a sufficient condition for a self-adjoint operator to have the following properties in a neighborhood of a pointE of its spectrum:

1. its point spectrum is finite;
2. its singular continuous spectrum is empty;
3. its resolvent satisfies a class of a priori estimates.

     

Nachwirkungsmechanismen in Ferriten

In ferrites a large number of after-effects are found, with time constants between nano-seconds and years. In this review the after-effects due to ion-and electron motion will be treated. One finds:

1. single-ion effects in combination with lattice deformations, e.g. Mn³⁺;
2. ion effects caused by mobile vacancies, e.g. Co²⁺;
3. effects due to electron transfer:
4. Co²⁺?Co³⁺
5. Me²⁺?Fe³⁺, in combination with Me⁴⁺ and vacancies.
6. Me⁴⁺?Fe²⁺, with Me=Si, Ti (photomagnetic effect).

The electron transfer is found to be related to electrical effects. In analogy to the photoelectric effect, one has found that illumination produces changes in magnetic properties. Generally speaking, one has in ferrites as many problems with donors and acceptors as in other semiconductors. Information from magnetic measurements helps to elucidate their nature.     

Existence of phase transitions for quantum lattice systems

We prove that the following lattice systems:

1. anisotropic Heisenberg model,
2. Ising model with transverse magnetic field,
3. quantum lattice gas with hard cores extending over nearest neighbours,

exhibit phase transitions if the temperature is sufficiently low and the transverse (or kinetic) part of the interaction sufficiently small.     

Dynamical enhanced electron emission and discharges at contaminated surfaces

Broad-area electrodes show electron emission already at electric field strengthsF≈10⁷ V/m. This enhanced field emission (EFE) occurs only for contaminated surfaces. EFE is accompanied by photon emission and gas desorption yielding finally discharges. EFE is caused by dust and contaminants initiating the following effects:

an electron is stochastically emitted in a trigger zone

the electron gains energyΔE?eΔxF ^*

which excites electronic states

which relax by the emission of electrons, photons, and atoms

where the positive charges left behind enhanceF ^*=βF (β?1) initiating so an electron avalanche, i.e., a high conductivity channel. Because of charge migration and neutralization, this avalanche has a life time. This pulsating EFE is accompanied by light emission and gas desorption yielding finally a gas cloud and a discharge.

The pulsating, self-sustained EFE has the same root as:

the enhanced secondary emission found first by Malter

the conductivity switching exhibited by thin (≈ 1 μm) layers of semiconductors or insulators

the normal cathode fall and

the firing-wave instability in neurodynamics.

     

The possibility of using a semiconductor thermal probe to investigate the power flow distribution in waveguides

Conclusions

1. The temperature profile of an absorbing film for a given microwave power flux distribution has been considered.
2. The conditions under which agreement is found between the temperature relief and the flux distribution has been clarified.
3. An experimental investigation has been carried out of the temperature profile in a matched film for the TE₁₀ mode.
4. The possibility of using a semiconductor thermal probe to investigate the microwave power flux distribution has been demonstrated.

     

Three applications toSO(4) invariant systems of a theorem of L. Michel relating extremal points to invariance properties

We consider a theorem due to Michel [1] which relates the invariance properties in peculiar directions in a linear space on which we represent a Lie groupG to the extremal points of an arbitrary smoothG-invariant function. The group we are interested in isSO(4) and we apply the mathematical results to the following problems:

1. mixed linear Stark Zeeman effect in a hydrogen atom,
2. perturbation of a finite Robertson-Walker metric,
3. gas evolutions preserving angular momentum and vorticity.

     

New interferometric method for determining the refractive index of thin dielectric film,its thickness,the phase shift,and the order of interference

A new interferometric method is proposed, using white light fringes of equal chromatic order to determine simultaneously the following paramcters:

1. The refractive index of a thin dielectric film, and hence its dispersion.
2. The film thickness.
3. The correct value of the order of interference.
4. The phase shift occuring due to reflection at the dielectric/metal interface. In the present work, doubly silvered zinc sulphide (ZnS) thin dielectric film was used as an example in applying the proposed method.

     

Two-dimensional quantum field theories containing a massless scalar field

The following new findings are briefly reported:

1. A consistent quantum theory can be formulated for a free massless scalar field in two-dimensional spacetime.
2. Satisfactory operator solutions in terms of asymptotic fields can be constructed in the Thirring and Schwinger models.
3. Gauge invariance is spontaneously broken in the Thirring model as well as in the Schwinger model.

     

Quasi-particles at finite temperatures

We study the consequences of the KMS-condition on the properties of quasi-particles, assuming their existence. We establish

1. If the correlation functions decay sufficiently, we can create them by quasi-free field operators.
2. The outgoing and incoming quasi-free fields coincide, there is no scattering.
3. There are may age-operatorsT conjugate toH. For special forms of the dispersion law ε(k) of the quasi-particles there is aT commuting with the number of quasi-particles and its time-monotonicity describes how the quasi-particles travel to infinity.

     

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.

     

Small-angle X-ray scattering on spinodal,nucleotic or coarsening processes in two-phase systems containing spherical,fibrillar or lamellar inhomogeneities

We study the effects of some of the most important and typical structural changes in two-phase systems on selected structural parameters obtained from small-angle x-ray scattering (SAXS) measurements. To limit the present study, it was assumed that the Phase, 1, embedded in the matrix

1. is monodispersed and homogeneous,
2. possesses one of the three most extreme shapes (spherical, fibrillar or lamellar) and
3. changes its behaviour

1. through type change (spinodal or nucleotic or coarsening), without changing the shape,
2. through a change of the shape only, or
3. through a) (type change) and b) (shape change) simultaneously.

To find the type of change for three basically different shapes of Phase 1 and to calculate its intensity (amount of the change) the following three SAXS parameters must be compared before and after the treatment of the system:

1. chord lengthl ₁ (and/or radius of gyrationR),
2. volume partw ₁ of the Phase 1, and
3. relative inner surfaceS _v of the system.

It is shown by this comparison that by the pure type change in the case of

1. spinodal change, all three SAXRS parameters are increasing or decreasing simultaneously and proportional to a power of the intensity of the change,
2. nucleotic change,l ₁ (and/orR) is unchanged, the other two (w ₁ andS _v ) are increasing or decreasing simultaneously and directly proportional to the intensity,
3. coarsening change,w ₁ is unchanged and anincreasing ofl ₁ is always accompanied by adecreasing ofS _v and vice versa.

In addition to this type change, the cases of mere changes of the shape (“shape change”) and finally of simultaneous type and/or shape change are studied. For the case of pure shape change the alteration of the dimensions (chord lengthl ₁ and/or radius of gyrationR) must be followed. The limitations of the analyses of the simultaneous type and/or shape change are discussed in detail.     

Optimal escape from circular orbits around black holes

An obvious strategy to escape from a stable circular orbit in the Schwarzschild spacetime is to employ a tangential instantaneous acceleration. Using the theory of optimal rocket trajectories in general relativity, recently developed in Henriques and Natário (J Optim Theory Appl 154:500–552; 2011), we show that this manoeuvre satisfies the optimality conditions for maximizing the rocket’s final energy (given a fixed amount of fuel) if and only if the magnitude of the acceleration is smaller than a certain bound. This is the general relativistic version of a result by Lawden (J Brit Interplan Soc 12:68–71; 1953).     

On the existence of crossing symmetric and unitary scattering amplitudes with Regge poles

We give a complete proof of the existence of scattering amplitudesA(s,t,u) with the following properties

1. the amplitudes are total symmetric ins,t, andu.
2. they satisfy elastic unitarity for 4≦s≦16, and
3. they develop resonances forl≧2 on a bounded Regge trajectory which dominates the asymptotics for large energies.

     

Dragged metrics

We show that the path of any accelerated body in an arbitrary spacetime geometry $g_{\mu \nu }$ can be described as a geodesic in a dragged metric $\hat{q}_{\mu \nu }$ that depends only on the background metric and on the motion of the body. Such procedure allows the interpretation of all kinds of non-gravitational force as modifications of the spacetime metric. This method of effective elimination of the forces by changing the metric of the substratum can be understood as a generalization of the d’Alembert principle applied to all relativistic processes.