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Sufficient and necessary conditions for causal localizations of massive relativistic systems are developed. It is proven that the Dirac-and the Dirac tensor-system are up to unitary equivalence the only irreducible causal localizations with finite spinor dimension which have a massive relativistic extension. A formula for this extension is given. The existence of arbitrarily good localized states of positive energy is shown. In the context of the causality condition a Paley-Wiener theorem for bounded measurable matrix-valued functions is proven.iii ZusammenfassungHinreichende und notwendige Bedingungen für kausale Lokalisierungen massiver relativistischer Systeme werden entwickelt. Bewiesen wird, dass das Dirac-und das Dirac Tensor-System bis auf unitäre Äquivalenz die einzigen irreduziblen kausalen Lokalisierungen mit endlicher Spinor Dimension sind, die eine massive relativistische Fortsetzung besitzen. Eine Formel für diese Fortsetzung wird angegeben. Die Existenz beliebig gut lokalisierbarer Zustände positiver Energie wird gezeigt. Im Kontext der Kausalitätsbedingung wird ein Paley-Wiener Satz für beschränkte messbare matrixwertige Funktionen bewiesen.iv

The well-known treatment of the path integral for the Coulomb potential, by means of the Kustaanheimo–Stiefel transformation and a time transformation, is made more transparent by reducing the problem to the equality of two measures on the space of paths. For this equality two proofs are given: an elementary computational one and a short one recurring to general features of stochastic processes. It is shown that the time transformation is a special case of the well-known time change for a continuous local martingale, by which the process is changed to a Brownian motion and which is determined by its quadratic variation.

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