Abstract:
We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out two examples of Hamiltonian invariance under such symmetries. The Schrodinger equation for a free particle is investigated in such a non-commutative plane and a connection with anyonic statistics is found.

Abstract:
Using a multipole expansion of the radiated field generated by a classical electric current, we present a way to interprete the bremsstrahlung spectra of low energy heavy ion collisions. We perform the calculation explicitely for the system ^{12}C+ ^{12}C at 84AMeV and compare the result with the experimental data of E. Grosse et al. Using simple model assumptions for the electromagnetic source current we are able to describe the measured data in terms of coherent photon emission. In this context, the information contained in the measured data is discussed.

Abstract:
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific conditions. A pseudo-complex Schwarzschild solution is constructed, which does not suffer any more by a singularity. The solution indicates a minimal radius for a heavy mass object. Consequences for the redshift and possible signatures for its observation are discussed.

Abstract:
In this article we compute the density of Dirac particles created by a cosmological anisotropic Bianchi I universe in the presence of a constant electric field. We show that the particle distribution becomes thermal when one neglects the electric interaction.

Abstract:
We compute the probabilty for the processes A -> q \bar{q}, gg via vacuum polarization in the presence of a classical space-time dependent non-abelian field A by applying the background field method of QCD. The processes we consider are leading order in gA and are simillar to A -> e^+e^- in QED. Gluons are treated like a matter field and gauge transformations of the quantum gluonic field are different from those of the classical chromofield. To obtain the correct physical polarization of gluons we deduct the corresponding ghost contributions. We find that the expression for the probability of the leading order process A -> gg is transverse with respect to the momentum of the field. We observe that the contributions from higher order processes to gluon pair production need to be added to the this leading order process. Our result presented here is a part of the expression for the total probability for gluon pair production from a space-time dependent chromfield. The result for q \bar{q} pair production is similar to that of the e^+e^- pair production in QED. Quark and gluon production from a space-time dependent chromofield will play an important role in the study of the production and equilibration of the quark-gluon plasma in ultra relativistic heavy-ion collisions.

Abstract:
In this article we compute the density of scalar and Dirac particles created by a cosmological anisotropic Bianchi type I universe in the presence of a time varying electric field. We show that the particle distribution becomes thermal when one neglects the electric interaction.

Abstract:
We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for supercriticality.

Abstract:
We study different realisations of the first order deconfinement phase transition inside a compact star by comparing the Gibbs and Maxwell construction for the mixed phase. The hadronic sector is described within the relativistic mean field model including hyperons. The quark sector is described by the MIT Bag model. We find that these two realisations lead to very different star properties, in particular, the composition of the stellar matter. We also find that for the Maxwell construction there is a sharp discontinuity in the baryon density and the electron chemical potential. We argue that a sharp jump in the elctron chemical potential should lead to the redistribution of electrons and formation of strong electric fields around the discontinuity surface.

Abstract:
Due to a first order phase transition, a compact star may have a discontinuous distribution of baryon as well as electric charge densities, as e.g. at the surface of a strange quark star. The induced separation of positive and negative charges may lead to generation of supercritical electric fields in the vicinity of such a discontinuity. We study this effect within a relativistic Thomas-Fermi approximation and demonstrate that the strength of the electric field depends strongly on the degree of sharpness of the surface. The influence of strong electric fields on the stability of compact stars is discussed. It is demonstrated that stable configurations appear only when the counter-pressure of degenerate fermions is taken into consideration.

Abstract:
We study the propagation of nucleons and nuclei in tissue-like media within a Monte Carlo Model for Heavy-ion Therapy (MCHIT) based on the GEANT4 toolkit (version 8.2). The model takes into account fragmentation of projectile nuclei and secondary interactions of produced nuclear fragments. Model predictions are validated with available experimental data obtained for water and PMMA phantoms irradiated by monoenergetic carbon-ion beams. The MCHIT model describes well (1) the depth-dose distributions in water and PMMA, (2) the doses measured for fragments of certain charge, (3) the distributions of positron emitting nuclear fragments produced by carbon-ion beams, and (4) the energy spectra of secondary neutrons measured at different angles to the beam direction. Radial dose profiles for primary nuclei and for different projectile fragments are calculated and discussed as possible input for evaluation of biological dose distributions. It is shown that at the periphery of the transverse dose profile close to the Bragg peak the dose from secondary nuclear fragments is comparable to the dose from primary nuclei.