The non-unique Universe

The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of Godel's incompleteness theorem for theories of everything. Three conclusions are obtained in the final section: (i) the theory of the structure of our universe might be an undecidable theory, and this constitutes a potential epistemological limit for mathematical physics, but because such a theory must be complete, there is no ontological barrier to the existence of a final theory of everything; (ii) in terms of mathematical logic, there are two different types of multiverse: classes of non-isomorphic but elementarily equivalent models, and classes of model which are both non-isomorphic and elementarily inequivalent; (iii) for a hypothetical theory of everything to have only one possible model, and to thereby negate the possible existence of a multiverse, that theory must be such that it admits only a finite model

Parton Distributions in the Valon Model

The parton distribution functions determined by CTEQ at low $Q^2$ are used as inputs to test the validity of the valon model. The valon distributions in a nucleon are first found to be nearly $Q$ independent. The parton distribution in a valon are shown to be consistent with being universal, independent of the valon type. The momentum fractions of the partons in the valon add up separately to one. These properties affirm the validity of the valon model. The various distributions are parameterized for convenient application of the model.Comment: 9 pages + 9 figures in ep

Inclusive particle production at HERA: Higher-order QCD corrections to the resolved quasi-real photon contribution

We calculate in next-to-leading order inclusive cross sections of single-particle production via resolved photons in $ep$ collisions at HERA. Transverse-momentum and rapidity distributions are presented and the scale dependence is studied. The results are compared with first experimental data from the H1 Collaboration at HERA.Comment: 11 pages with 15 uuencoded PS figures. Preprint DESY 93-03

Solving non-uniqueness in agglomerative hierarchical clustering using multidendrograms

In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which we call a multidendrogram, as well as a generalization of the Lance and Williams' formula which enables the implementation of the algorithm in a recursive way.Comment: Free Software for Agglomerative Hierarchical Clustering using Multidendrograms available at http://deim.urv.cat/~sgomez/multidendrograms.ph

Pinning down the Glue in the Proton

The latest measurements of $F_2$ at HERA allow for a {\it combination} of gluon and sea quark distributions at small $x$ that is significantly different from those of existing parton sets. We perform a new global fit to deep-inelastic and related data. We find a gluon distribution which is larger for x \lapproxeq 0.01, and smaller for $x \sim 0.1$, and a flatter input sea quark distribution than those obtained in our most recent global analysis. The new fit also gives $\alpha_s(M_Z^2) = 0.114$. We study other experimental information available for the gluon including, in particular, the constraints coming from fixed-target and collider prompt $\gamma$ production data.Comment: 8 pages, LATEX, 6 figs available as .uu fil

Quantum coherence in a degenerate two-level atomic ensemble: for a transition Fe=0↔Fg=1F_e=0\leftrightarrow F_g=1

For a transition $F_e=0\leftrightarrow F_g=1$ driven by a linearly polarized light and probed by a circularly light, quantum coherence effects are investigated. Due to the coherence between the drive Rabi frequency and Zeeman splitting, electromagnetically induced transparency, electromagnetically induced absorption, and the transition from positive to negative dispersion are obtained, as well as the populations coherently oscillating in a wide spectral region. At the zero pump-probe detuning, the subluminal and superluminal light propagation is predicted. Finally, coherent population trapping states are not highly sensitive to the refraction and absorption in such ensemble.Comment: 9 pages, 6 figure

Representation theory of super Yang-Mills algebras

We study in this article the representation theory of a family of super algebras, called the \emph{super Yang-Mills algebras}, by exploiting the Kirillov orbit method \textit{\`a la Dixmier} for nilpotent super Lie algebras. These super algebras are a generalization of the so-called \emph{Yang-Mills algebras}, introduced by A. Connes and M. Dubois-Violette in \cite{CD02}, but in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras \Cliff_{q}(k) \otimes A_{p}(k), for $p \geq 3$, or $p = 2$ and $q \geq 2$, appear as a quotient of all super Yang-Mills algebras, for $n \geq 3$ and $s \geq 1$. This provides thus a family of representations of the super Yang-Mills algebras

Magnetic Fields Produced by Phase Transition Bubbles in the Electroweak Phase Transition

The electroweak phase transition, if proceeding through nucleation and growth of bubbles, should generate large scale turbulent flow, which in turn generates magnetic turbulence and hence magnetic fields on the scale of turbulent flow. We discuss the seeding of this turbulent field by the motion of the dipole charge layers in the phase transition bubble walls, and estimate the strength of the produced fields.Comment: Revtex, 14 pages, 3 figures appended as uuencoded postscript-fil

Noncommutative resolutions of ADE fibered Calabi-Yau threefolds

In this paper we construct noncommutative resolutions of a certain class of Calabi-Yau threefolds studied by F. Cachazo, S. Katz and C. Vafa. The threefolds under consideration are fibered over a complex plane with the fibers being deformed Kleinian singularities. The construction is in terms of a noncommutative algebra introduced by V. Ginzburg, which we call the "N=1 ADE quiver algebra"

Inflationary models inducing non-Gaussian metric fluctuations

We construct explicit models of multi-field inflation in which the primordial metric fluctuations do not necessarily obey Gaussian statistics. These models are realizations of mechanisms in which non-Gaussianity is first generated by a light scalar field and then transferred into curvature fluctuations. The probability distribution functions of the metric perturbation at the end of inflation are computed. This provides a guideline for designing strategies to search for non-Gaussian signals in future CMB and large scale structure surveys.Comment: 4 pages, 7 figure