Non-Standard Fermion Propagators from Conformal Field Theory

It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of half-integer conformal weights. This yields representations of fermionic 2-point functions in terms of correlators of primary fields with a factorized transformation behavior under the Lorentz group. I employ this observation to determine the general structure of the corresponding Lorentz covariant correlators by methods similar to the methods employed in conformal field theory to determine 2- and 3-point functions of primary fields. In particular, the chiral symmetry breaking terms resemble fermionic 2-point functions of 2D CFT up to a function of the product of momenta. The construction also permits for the formulation of covariant meromorphy constraints on spinors in 3+1 dimensions.Comment: 15 pages, Latex, LMU-TPW 94-1

Non-Vanishing Cosmological Constant Λ\Lambda, Phase Transitions, And Λ\Lambda-Dependence Of High Energy Processes

It is pointed out that a collider experiment involves a local contribution to the energy-momentum tensor, a circumstance which not a common feature of the current state of the Universe at large characterized by the cosmological constant $\Lambda_0$. This contribution may be viewed as a change in the structure of space-time from its large scale form governed by $\Lambda_0$ to one governed by a $\Lambda$ peculiar to the scale of the experiment. Possible consequences of this effect are explored by exploiting the asymptotic symmetry of space-time for non-vanishing $\Lambda$ and its relation to vacuum energy.Comment: 11 pages; UCTP101.02; last section revised; the version to appear in Physics Letters

Family Dependence in SU(3)_C X SU(3)_L X U(1)_X models

Using experimental results at the Z-pole and atomic parity violation, we perform a chi-squared fit at 95% CL to obtain family-dependent bounds to Z_2 mass and Z-Z' mixing angle in the framework of SU(3)_C X SU(3)_L X U(1)_X models. The allowed regions depend on the assignment of the quark families in mass eigenstates into the three different families in weak eigenstates that cancel anomaliesComment: 14 pages, 2 figures, LaTeX2e; added references, added equations with electroweak corrections for section 4. Version to appear in Phys. Rev.

Hard rods: statistics of parking configurations

We compute the correlation function in the equilibrium version of R\'enyi's {\sl parking problem}. The correlation length is found to diverge as $2^{-1}\pi^{-2}(1-\rho)^{-2}$ when $\rho\nearrow1$ (maximum density) and as $\pi^{-2}(2\rho-1)^{-2}$ when $\rho\searrow1/2$ (minimum density).Comment: 9 pages, 1 figur

Spin and Rotation in General Relativity

Rapporteur's Introduction to the GT8 session of the Ninth Marcel Grossmann Meeting (Rome, 2000); to appear in the Proceedings.Comment: LaTeX file, no figures, 15 page

Four Dimensional Integrable Theories

There exist many four dimensional integrable theories. They include self-dual gauge and gravity theories, all their extended supersymmetric generalisations, as well the full (non-self-dual) N=3 super Yang-Mills equations. We review the harmonic space formulation of the twistor transform for these theories which yields a method of producing explicit connections and metrics. This formulation uses the concept of harmonic space analyticity which is closely related to that of quaternionic analyticity. (Talk by V. Ogievetsky at the G\"ursey Memorial Conference I, Istanbul, June 1994)Comment: 11 pages, late

On Beltrami Model of de Sitter Spacetime

Based on some important properties of $dS$ space, we present a Beltrami model ${\cal B}_\Lambda$ that may shed light on the observable puzzle of $dS$ space and the paradox between the special relativity principle and cosmological principle. In ${\cal B}_\Lambda$, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson-Walker-like metric. It is of positive spatial curvature of order $\Lambda$. This is more or less indicated already by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.Comment: 4 page

Physics of Quantum Relativity through a Linear Realization

The idea of quantum relativity as a generalized, or rather deformed, version of Einstein (special) relativity has been taking shape in recent years. Following the perspective of deformations, while staying within the framework of Lie algebra, we implement explicitly a simple linear realization of the relativity symmetry, and explore systematically the resulting physical interpretations. Some suggestions we make may sound radical, but are arguably natural within the context of our formulation. Our work may provide a new perspective on the subject matter, complementary to the previous approach(es), and may lead to a better understanding of the physics.Comment: 27 pages in Revtex, no figure; proof-edited version to appear in Phys.Rev.

Large Right Handed Rotations, Neutrino Oscillations and Proton Decay

Right Handed (RH) rotations are not observable in the standard model (SM). The freedom is used to give the phenomenologically correct mass matrices all kind of different forms and this is one of the reasons for the proliferation of models for the fermionic masses. The SM must be however extended and in most extensions, RH currents appear at higher energy scales. At those energies the RH rotations are not irrelevant any more, they can affect neutrino oscillations, proton decay, baryon assymetry, R-parity violating interactions etc. We study possible implications of large RH mixing in GUTs. Those are interesting not only because large mixing induce large effects. They are intimately related to large lepton mixing in GUTs, via a relation between LH mixing of the leptons and the RH ones of the d-quarks ,(``$d - \ell$ duality'') and can change considerably the branching ratios of proton decay. Observation of proton decay channels as well as neutrino oscillations will teach us about RH rotations and will reduce, therefore, considerably the freedom in the fermionic mass matrices. Some interesting examples are studied in detail. In particular a new $E_6$ model which realizes naturally a $d$ - $\ell$ duality by mixing with exotic $E_6$ fermions.Comment: 7 pages, no figuers; talk at the TAUP99, to be published in JHEP; LaTeX margins correcte

The general classical solution of the superparticle

The theory of vectors and spinors in 9+1 dimensional spacetime is introduced in a completely octonionic formalism based on an octonionic representation of the Clifford algebra \Cl(9,1). The general solution of the classical equations of motion of the CBS superparticle is given to all orders of the Grassmann hierarchy. A spinor and a vector are combined into a $3 \times 3$ Grassmann, octonionic, Jordan matrix in order to construct a superspace variable to describe the superparticle. The combined Lorentz and supersymmetry transformations of the fermionic and bosonic variables are expressed in terms of Jordan products.Comment: 11 pages, REVTe