On an easy transition from operator dynamics to generating functionals by Clifford algebras

Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that opposite Clifford algebras have to be used also. Based on this mathematics, we give a fully Clifford algebraic account on generating functionals, which is thereby geometric. The field operators are shown to be Clifford and opposite Clifford maps. This picture relying on geometry does not need positivity in principle. Furthermore, we propose a transition from operator dynamics to corresponding generating functionals, which is based on the algebraic techniques. As a calculational benefit, this transition is considerable short compared to standard ones. The transition is not injective (unique) and depends additionally on the choice of an ordering. We obtain a direct and constructive connection between orderings and the explicit form of the functional Hamiltonian. These orderings depend on the propagator of the theory and thus on the ground state. This is invisible in path integral formulations. The method is demonstrated within two examples, a non-linear spinor field theory and spinor QED. Antisymmetrized and normal-ordered functional equations are derived in both cases.Comment: 23p., 76kB, plain LaTeX, [email protected]

Dark matter powered stars: Constraints from the extragalactic background light

The existence of predominantly cold non-baryonic dark matter is unambiguously demonstrated by several observations (e.g., structure formation, big bang nucleosynthesis, gravitational lensing, and rotational curves of spiral galaxies). A candidate well motivated by particle physics is a weakly interacting massive particle (WIMP). Self-annihilating WIMPs would affect the stellar evolution especially in the early universe. Stars powered by self-annihilating WIMP dark matter should possess different properties compared with standard stars. While a direct detection of such dark matter powered stars seems very challenging, their cumulative emission might leave an imprint in the diffuse metagalactic radiation fields, in particular in the mid-infrared part of the electromagnetic spectrum. In this work the possible contributions of dark matter powered stars (dark stars; DSs) to the extragalactic background light (EBL) are calculated. It is shown that existing data and limits of the EBL intensity can already be used to rule out some DS parameter sets.Comment: Accepted for publication in ApJ; 7 pages, 5 figure

Dark Stars: Improved Models and First Pulsation Results

We use the stellar evolution code MESA to study dark stars. Dark stars (DSs), which are powered by dark matter (DM) self-annihilation rather than by nuclear fusion, may be the first stars to form in the Universe. We compute stellar models for accreting DSs with masses up to 10^6 M_{sun}. The heating due to DM annihilation is self-consistently included, assuming extended adiabatic contraction of DM within the minihalos in which DSs form. We find remarkably good overall agreement with previous models, which assumed polytropic interiors. There are some differences in the details, with positive implications for observability. We found that, in the mass range of 10^4 -10^5 M_{sun}, our DSs are hotter by a factor of 1.5 than those in Freese et al.(2010), are smaller in radius by a factor of 0.6, denser by a factor of 3 - 4, and more luminous by a factor of 2. Our models also confirm previous results, according to which supermassive DSs are very well approximated by (n=3)-polytropes. We also perform a first study of dark star pulsations. Our DS models have pulsation modes with timescales ranging from less than a day to more than two years in their rest frames, at z ~ 15, depending on DM particle mass and overtone number. Such pulsations may someday be used to identify bright, cool objects uniquely as DSs; if properly calibrated, they might, in principle, also supply novel standard candles for cosmological studies.Comment: 17 pages; 11 figures; revised version; accepted by Ap

Inflation From Symmetry Breaking Below the Planck Scale

We investigate general scalar field potentials \hbox{$V\left(\phi\right)$} for inflationary cosmology arising from spontaneous symmetry breaking. We find that potentials which are dominated by terms of order $\phi^m$ with \hbox{$m > 2$} can satisfy observational constraints at an arbitrary symmetry breaking scale. Of particular interest, the spectral index of density fluctuations is shown to be independent of the specific form of the potential, depending only on the order $m$ of the lowest non-vanishing derivative of $V(\phi)$ near its maximum. The results of a model with a broken ${\rm SO(3)}$ symmetry illustrate these features.Comment: Submitted to Phys. Rev. Letters. 7 Pages, REVTeX. No figure

My Lady Chlo : African Love Song

https://digitalcommons.library.umaine.edu/mmb-vp/2194/thumbnail.jp