A geometric basis for the standard-model gauge group

A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into left-sided ("exterior") and right-sided ("interior") types. By definition, Poincare transformations are exterior ones. We consider all rotations in the seven-dimensional space that (1) conserve the spacetime components of the particle and antiparticle currents and (2) do not couple the right-chiral neutrino. These rotations comprise additional exterior transformations that commute with the Poincare group and form the group SU(2)_L, interior ones that constitute SU(3)_C, and a unique group of coupled double-sided rotations with U(1)_Y symmetry. The spinor mediates a physical coupling of Poincare and isotopic symmetries within the restrictions of the Coleman--Mandula theorem. The four extra spacelike dimensions in the model form a basis for the Higgs isodoublet field, whose symmetry requires the chirality of SU(2). The charge assignments of both the fundamental fermions and the Higgs boson are produced exactly.Comment: 17 pages, LaTeX requires iopart. Accepted for publication in J. Phys. A: Math. Gen. 9 Mar 2001. Typos correcte

Intense CIII] 1907,1909 emission from a strong Lyman continuum emitting galaxy

We have obtained the first complete ultraviolet (UV) spectrum of a strong Lyman continuum(LyC) emitter at low redshift -- the compact, low-metallicity, star-forming galaxy J1154+2443 -- with a Lyman continuum escape fraction of 46% discovered recently. The Space Telescope Imaging Spectrograph spectrum shows strong Lya and CIII] 1909 emission, as well as OIII] 1666. Our observations show that strong LyC emitters can have UV emission lines with a high equivalent width (e.g. EW(CIII])$=11.7 \pm 2.9 \AA$ rest-frame), although their equivalent widths should be reduced due to the loss of ionizing photons. The intrinsic ionizing photon production efficiency of J1154+2443 is high, $\log(\xi_{\rm ion}^0)=25.56$ erg$^{-1}$ Hz, comparable to that of other recently discovered $z \sim 0.3-0.4$ LyC emitters. Combining our measurements and earlier determinations from the literature, we find a trend of increasing $\xi_{\rm ion}^0$ with increasing CIII] 1909 equivalent width, which can be understood by a combination of decreasing stellar population age and metallicity. Simple ionization and density-bounded photoionization models can explain the main observational features including the UV spectrum of J1154+2443.Comment: 5 pages, 4 figures. Accepted for publication in A&A Letter

Accurately predicting the escape fraction of ionizing photons using restframe ultraviolet absorption lines

The fraction of ionizing photons that escape high-redshift galaxies sensitively determines whether galaxies reionized the early universe. However, this escape fraction cannot be measured from high-redshift galaxies because the opacity of the intergalactic medium is large at high redshifts. Without methods to indirectly measure the escape fraction of high-redshift galaxies, it is unlikely that we will know what reionized the universe. Here, we analyze the far-ultraviolet (UV) H I (Lyman series) and low-ionization metal absorption lines of nine low-redshift, confirmed Lyman continuum emitting galaxies. We use the H I covering fractions, column densities, and dust attenuations measured in a companion paper to predict the escape fraction of ionizing photons. We find good agreement between the predicted and observed Lyman continuum escape fractions (within $1.4\sigma$) using both the H I and ISM absorption lines. The ionizing photons escape through holes in the H I, but we show that dust attenuation reduces the fraction of photons that escape galaxies. This means that the average high-redshift galaxy likely emits more ionizing photons than low-redshift galaxies. Two other indirect methods accurately predict the escape fractions: the Ly$\alpha$ escape fraction and the optical [O III]/[O II] flux ratio. We use these indirect methods to predict the escape fraction of a sample of 21 galaxies with rest-frame UV spectra but without Lyman continuum observations. Many of these galaxies have low escape fractions ($f_{\rm esc} \le 1$\%), but 11 have escape fractions $>1$\%. The methods presented here will measure the escape fractions of high-redshift galaxies, enabling future telescopes to determine whether star-forming galaxies reionized the early universe.Comment: Accepted for publication in A&A. 12 pages, 5 figure

Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime

A theory in which 4-dimensional spacetime is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza-Klein theory. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U(1)xSU(2)xSU(3) of the standard model. The generalized spin connection in C-space has the properties of Yang-Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb-Ramond fields.Comment: 57 pages; References added, section 2 rewritten and expande

The exponential map for the unitary group SU(2,2)

In this article we extend our previous results for the orthogonal group, $SO(2,4)$, to its homomorphic group $SU(2,2)$. Here we present a closed, finite formula for the exponential of a $4\times 4$ traceless matrix, which can be viewed as the generator (Lie algebra elements) of the $SL(4,C)$ group. We apply this result to the $SU(2,2)$ group, which Lie algebra can be represented by the Dirac matrices, and discuss how the exponential map for $SU(2,2)$ can be written by means of the Dirac matrices.Comment: 10 page

Field diffeomorphisms and the algebraic structure of perturbative expansions

We consider field diffeomorphisms in the context of real scalar field theories. Starting from free field theories we apply non-linear field diffeomorphisms to the fields and study the perturbative expansion for the transformed theories. We find that tree level amplitudes for the transformed fields must satisfy BCFW type recursion relations for the S-matrix to remain trivial. For the massless field theory these relations continue to hold in loop computations. In the massive field theory the situation is more subtle. A necessary condition for the Feynman rules to respect the maximal ideal and co-ideal defined by the core Hopf algebra of the transformed theory is that upon renormalization all massive tadpole integrals (defined as all integrals independent of the kinematics of external momenta) are mapped to zero.Comment: 8 pages, 2 figure