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Based on the nowadays available phenomenological multipoles for pion photoproduction, a systematic dispersion theoretic calculation of Compton partial amplitudes has been performed. By comparing with the new experimental data in the Δ(1232) region it is found that the hitherto existing discrepancies between the data and theory remain. Our results allow us to isolate the basis of this problem. It is due to the fact that the imaginary parts of the Compton amplitudes determined already by unitarity, give too large contributions to the cross section thus leaving no space for real parts required by the dispersion integrals. Therefore a simultaneous partial-wave analysis for Compton scattering and pion photoproduction was carried through employing only the unitarity connections between both. The resulting amplitudes give a good fit to the Compton cross section and all photoproduction data; moreover the photoproduction multipoles agree essentially with those of the previous analyses. On the other hand for Compton scattering, phenomenological amplitudes are obtained for the first time and a model independent test of dispersion theoretic amplitudes can be carried out. For the resonating fMM1+ amplitude which describes the M1 excitation and deexcitation to the Δ-isobar, large discrepancies have been found. Possible consequences especially for the forward scattering amplitude and the validity of the Kramers-Kronig relation are discussed.

The formulation of operator gange transformations is discussed. Using some simple consequences of charge conservation and the equal time commutation relations it is possible to give an exact meaning to a certain class of such transformations. This class contains all the special cases which have obtained importance for practical calculations. Only renormalized Heisenberg operators are used throughout.

It is shown in this paper, that it is possible to construct parity conserving baryonpion interactions which areγ-invariant in exactly the same manner as electromagnetic and weak interactions.

Die Kennzeichnung der radioaktiven Zustande durch die Pole derS-Funktion wird mit den Ergebnissen der fruheren Arbeit des Verfassers [7] verglichen. Dazu werden furr≧a verschwindenden Potentiale untersucht. Es ergibt sich, da\ dieS-Funktion dafur unendlich viele gemischt-komplexe Pole besitzt, von denen aber nur endlich viele tatsachlich physikalisch bemerkbar sein konnen

The asymptotic conditions for the field operators are used in order to employ only renormalized quantities in quantum electrodynamics and to avoid the usual procedure of adiabatic switching off of the interaction. The treatment is based mainly on invariance properties and therefore gives a somewhat simpler formulation of the renormalization procedure.

The Weizsacker-Williams method is discussed using modern techniques. It is shown how gauge invariance guarantees the vanishing of the longitudinal cross-section for zero momentum-transfer. Explicit calculations are carried out for virtual Compton scattering and applied to determine the radiative corrections due to hard photons in muon-electron scattering.

The predictions of reggeized vector meson exchange in γp→pπo are discussed. For t small, the calculated ω- exchange agrees with available data. The theoretical minimum at t = -0.6 (GeV/c)2 is tentatively removed at 2 GeV by a resonant background.

Die bisherige allgemeine Theorie von Regelsystemen wird dadurch verallgemeinert, das fur die Regelstarke eine zeitliche Variation zugelassen wird, die das System in einem endlichen Zeitintervall in den gewunschten End-zustand uberfuhrt. Die Losung dieses Problems gelingt mit Hilfe einer allgemeinen Laplace-Transformation. Unter der Voraussetzung, das die auftretenden Differential-Operatoren Polynome beliebigen, aber endlichen Grades sind, werden die strengen Losungen in Integralform aufgeschrieben und asymptotische Entwicklungen sowie Potenzreihen daraus gefolgert. Auserdem werden die Bedingungen fur die Stabilitat des Regelsystems angegeben. Eine Anwendung der Formeln soll in einer spateren Arbeit erfolgen. The existing general theory of servomechanism is generalized so as to cover systems where the control strength varies with time in such a way that the system is brougth into the prescribed final state within a finite period of time. The problem is solved by using a general Laplace transformation. For the case that the differential operators are polynoms of any finite degree rigorous solutions in integral form are given from which asymptotic expansion and power series are derived. The stability conditions of the system are also derived. Applications will be dealt with in a forthcoming paper.

Das von den Verfassern in der fruheren Arbeit [1] gestellte Regelproblem mit zeitlich variabler Regelstarke wird vollstandig gelost. Dazu wird. 1. der Einflus einer auseren Kraft durch Berechnung des entsprechenden partikularen Integrals bestimmt und. 2. der Fehler ermittelt, der bei beliebig vorgegebenen Anfangsbedingungen des Systems, zur Zeit t = 0 besteht, wo das System den gewunschten Endzustand erreicht haben soll. The problem of servomechanism with variable control strength which has been posed in a previous paper [1] is now solved completely by. 1. determining the influence of an external force by means of the corresponding particular integral, and 2. determining the deviation from the prescribed end position at t = 0 for arbitrary initial conditions.

Es wird eine quantenmechanische Beschreibung der gebundenen Zustande fur die nichtrelativistische Bewegung in einem Potential angegeben, die sich zwangslos in das Kontinuum positiver Energien „fortsetzen“ la\t und hier die Stellen der Streumaxima auszeichnet. Dies gelingt mit Hilfe einer dimensionslosen Operatorschar, die im ganzen Energiebereich fur alle kernphysikalisch wichtigen Potentiale vollstetig ist. Die Form dieser Operatoren ermoglicht allgemeine Schlusse uber die Verteilung der Stellen maximaler Streuung und uber die funktionentheoretischen Eigenschaften derQ-Funktion. Abschlie\end folgt ein Vergleich mit den uberlegungen vonJost undPais [6] und derWignerschen „Dispersionstheorie“.

Theπ+−π0 mass difference is calculated from spectral function sum rules with finite widths ofρ and A1 The deviation from the zero width approximation is found to be small.