The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schr\"{o}dinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feyman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard "free" case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schr\"{o}dinger problem, the "free noise" can also be extended to any infinitely divisible probability law, as covered by the L\'{e}vy-Khintchine formula. Since the relativistic Hamiltonians $|\nabla |$ and $\sqrt {-\triangle +m^2}-m$ are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schr\"{o}dinger evolution is analyzed in detail. The relativistic covariance of related waveComment: Latex fil

Problem of the Pliocene/Pleistocene boundary in fresh-water deposits at Mizerna, West Carpathians

TheMizerna site (Polish Western Carpathians) is one of the most important Pliocene palaeobotanic sites in Central Europe. Its fresh-water deposits, laid down in a buried river valley, were studied in detail more than half a century ago in natural exposures and shallow boreholes, prior to partial drowning of the area by an artificial lake. The deposits yielded a very rich macrofossil plant collection elaborated in detail by Szafer (1954) who claimed that they represented a continuous succession of the Pliocene through Early Pleistocene plant communities. First palynological examination of the Mizerna deposits (by Oszast) was made more than half a century ago. Re-evaluation of stratigraphic and palaeoclimatic significance of macrofossil plant remains, along with a reassessment of palaeoenvironmental and sedimentary conditions during formation of the Mizerna fresh-water deposits, is in progress. This may help elucidate the problem whether the Mizerna sediments represent both the Pliocene and Early Pleistocene or, solely, the Pliocene successions

Geochronologic evidence for Early Cretaceous volcanic activity on Barton Peninsula, King George Island, Antarctica

Ages of six volcanic and plutonic rocks on Barton Peninsula, King George Island, were determined using 40Ar/39Ar and K-Ar isotopic systems. The 40Ar/39Ar and K-Ar ages of basaltic andesite and diorite range from 48 My to 74 My and systematically decrease toward the upper stratigraphic section. Two specimens of basaltic andesite which occur in the lowermost sequence of the peninsula, however, apparently define two distinct plateau ages of 52-53 My and 119-120 My. The latter is interpreted to represent the primary cooling age of basaltic andesite, whereas the former is interpreted as the thermally-reset age caused by the intrusion of Tertiary granitic pluton. The isochron ages calculated from the isotope correlation diagram corroborate our interpretation based on the apparent plateau ages. It is therefore likely that volcanism was active during the Early Cretaceous on Barton Peninsula. When the K-Ar ages of previous studies are taken into account with our result, the ages of basaltic andesite in the northern part of the Barton Peninsula are significantly older than those in the southern part. Across the north-west-south-east trending Barton fault bounding the two parts, there are significant differences in geochronologic and geologic aspects