Relativistic wave equations for interacting massive particles with arbitrary half-intreger spins

New formulation of relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins s interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of rank $n ($n=s-\frac12$) antisymmetric w.r.t. n pairs of indices, whose components are bispinors. The form of RWE is straightforward and free of inconsistencies associated with the other approaches to equations describing interacting higher spin particles

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A second fourth-order ordinary differential equation for the general Fourier coefficent is derived from an integral representation of the coefficient, and both differential equations are shown to be equivalent. Series solutions for the various Fourier coefficients are also given, mostly in terms of Legendre functions and Bessel/Hankel functions. These are derived from the closed form hypergeometric solutions or an integral representation, or both. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented

Multiple Transitions to Chaos in a Damped Parametrically Forced Pendulum

We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying $\omega_0$ (the natural frequency of the pendulum) and $A$ (the amplitude of the external driving force). As $A$ is increased, the SP will restabilize after its instability, destabilize again, and so {\it ad infinitum} for any given $\omega_0$. Its destabilizations (restabilizations) occur via alternating supercritical (subcritical) period-doubling bifurcations (PDB's) and pitchfork bifurcations, except the first destabilization at which a supercritical or subcritical bifurcation takes place depending on the value of $\omega_0$. For each case of the supercritical destabilizations, an infinite sequence of PDB's follows and leads to chaos. Consequently, an infinite series of period-doubling transitions to chaos appears with increasing $A$. The critical behaviors at the transition points are also discussed.Comment: 20 pages + 7 figures (available upon request), RevTex 3.

Generalized Brans-Dicke cosmology in the presence of matter and dark energy

We study the Generalized Brans-Dicke cosmology in the presence of matter and dark energy. Of particular interest for a constant Brans-Dicke parameter, the de Sitter space has also been investigated.Comment: 9 page

Cooling flow bulk motion corrections to the Sunyaev Zel'dovich effect

We study the influence of converging cooling flow bulk motions on the Sunyaev-Zel'dovich (SZ) effect. To that purpose we derive a modified Kompaneets equation which takes into account the contribution of the accelerated electron media of the cooling flow inside the cluster frame. The additional term is different from the usual kinematic SZ-effect, which depends linearly on the velocity, whereas the contribution described here is quadratic in the macroscopic electron fluid velocity, as measured in the cluster frame. For clusters with a large cooling flow mass deposition rate and/or a small central electron density, it turns out that this effect becomes relevant.Comment: accepted for publication in New Astronom

Disappearing Dark Matter in Brane World Cosmology: New Limits on Noncompact Extra Dimensions

We explore cosmological implications of dark matter as massive particles trapped on a brane embedded in a Randall-Sundrum noncompact higher dimension $AdS_5$ space. It is an unavoidable consequence of this cosmology that massive particles are metastable and can disappear into the bulk dimension. Here, we show that a massive dark matter particle (e.g. the lightest supersymmetric particle) is likely to have the shortest lifetime for disappearing into the bulk. We examine cosmological constraints on this new paradigm and show that disappearing dark matter is consistent (at the 95% confidence level) with all cosmological constraints, i.e. present observations of Type Ia supernovae at the highest redshift, trends in the mass-to-light ratios of galaxy clusters with redshift, the fraction of X-ray emitting gas in rich clusters, and the spectrum of power fluctuations in the cosmic microwave background. A best $2 \sigma$ concordance region is identified corresponding to a mean lifetime for dark matter disappearance of $15 \le \Gamma^{-1} \le 80$ Gyr. The implication of these results for brane-world physics is discussed.Comment: 7 pages, 7 figures, new cosmological constraints added, accepted for publication in PR

Soft parton radiation in polarized vector boson production: theoretical issues

Accurate measurement of spin-dependent parton distributions in production of electroweak bosons with polarized proton beams at the Relativistic Heavy Ion Collider depends on good understanding of QCD radiation at small transverse momenta $q_T$ of vector bosons. We present a theoretical formalism for small-$q_T$ resummation of the cross sections for production of virtual photons, W, and Z bosons, with the subsequent decay of these bosons into lepton pairs, for arbitrary longitudinal polarizations of the proton beams.Comment: 35 pages, 2 figures; minor modifications; bibliography references adde

Quantum gauge models without classical Higgs mechanism

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRS formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is explained without recourse to a Higgs(-Englert-Brout-Guralnik-Hagen-Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.Comment: 20 pages in two-column EPJC format, shortened version accepted for publication. For more details, consult version

The influence of magnetic fields on the Sunyaev Zel'dovich effect in clusters of galaxies

We study the influence of intracluster large scale magnetic fields on the thermal Sunyaev-Zel'dovich (SZ) effect. In a macroscopic approach we complete the hydrostatic equilibrium equation with the magnetic field pressure component. Comparing the resulting mass distribution with a standard one, we derive a new electron density profile. For a spherically symmetric cluster model, this new profile can be written as the product of a standard ($\beta$-) profile and a radius dependent function, close to unity, which takes into account the magnetic field strength. For non-cooling flow clusters we find that the observed magnetic field values can reduce the SZ signal by $\sim 10$ with respect to the value estimated from X-ray observations and the $\beta$-model. If a cluster harbours a cooling flow, magnetic fields tend to weaken the cooling flow influence on the SZ-effect.Comment: Accepted for publication in New Astronom

The composition of the protosolar disk and the formation conditions for comets

Conditions in the protosolar nebula have left their mark in the composition of cometary volatiles, thought to be some of the most pristine material in the solar system. Cometary compositions represent the end point of processing that began in the parent molecular cloud core and continued through the collapse of that core to form the protosun and the solar nebula, and finally during the evolution of the solar nebula itself as the cometary bodies were accreting. Disentangling the effects of the various epochs on the final composition of a comet is complicated. But comets are not the only source of information about the solar nebula. Protostellar disks around young stars similar to the protosun provide a way of investigating the evolution of disks similar to the solar nebula while they are in the process of evolving to form their own solar systems. In this way we can learn about the physical and chemical conditions under which comets formed, and about the types of dynamical processing that shaped the solar system we see today. This paper summarizes some recent contributions to our understanding of both cometary volatiles and the composition, structure and evolution of protostellar disks.Comment: To appear in Space Science Reviews. The final publication is available at Springer via http://dx.doi.org/10.1007/s11214-015-0167-