The Launching of La Belle Epoque of High Energy Physics and Cosmology

PREFACE

ABOUT THE GLOBAL FOUNDATION

CONTENTS

Systems of tightly knotted, linked, or braided flux tubes will have a universal mass-energy spectrum if the flux is quantized. We focus on a model of glueballs as knotted QCD flux tubes.

After an Introduction briefly describing the rise and fall of the three-zero texture of the Zee model, we discuss still-allowed two-zero textures for the Majorana three-neutrino mass matrix. Finally, a model with two right-handed neutrinos and two Dirac texture zeros is described (FGY model) which can relate CP violation in leptogenesis to CP violation in long-baseline neutrino oscillations.

We propose a unification of some fine-tuning problems – really in this article only the problem of why the weak scale is so small in energy compared to a presumed fundamental scale, being say the Planck scale – by postulating the zero or very small value of the cosmological constant not only for one but for several vacua. This postulate corresponds to what we have called the Multiple Point Principle, namely that there be many “vacuum” states with the same energy density. We further assume that 6 top quarks and 6 anti-top quarks can bind by Higgs exchange so strongly as to become tachyonic and form a condensate. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The two vacua distinguished by such a condensate will have the same cosmological constant provided the top Yukawa coupling is about 1.1 ± 0.2, in good correspondence with the experimental value. The further requirement that this value of the Yukawa coupling, at the weak scale, be compatible with the existence of a third vacuum, with a Higgs field expectation value of the order of the fundamental scale, enforces a hierarchical scale ratio between the fundamental and weak scales of order 10¹⁶ − 10²⁰.

No abstract received.

The early petite unification (PUT) of quarks and leptons at TeV scales with used as a constraint, necessitates the introduction of extra quarks and leptons with unconventional electric charges (up to 4/3 for the quarks and 2 for the leptons). This talk, in honor of Paul Frampton’s 60th birthday, will be devoted to the motivation and construction of models of early unification and to their implications, including the issues of rare decays and unconventional fermions.

We discuss extensions of the Standard Model through extending the electroweak gauge symmetry. An extended electroweak symmetry requires a list of extra fermionic and scalar states. The former is necessary to maintain cancellation of gauge anomalies, and largely fixed by the symmetry embedding itself. The latter is usually considered quite arbitrary, so long as a vacuum structure admitting the symmetry breaking is allowed. Anomaly cancellation may be used to link the three families of quarks and leptons together, given a perspective on flavor physics. It is illustrated lately that the kind of models may also have the so-called little Higgs mechanism incorporated. This more or less fixes the scalar sector and take care of the hierarchy problem, making such models of extended electroweak symmetries quite appealing candidates as TeV scale effective field theories.

Spacetime foam, also known as quantum foam, has its origin in quantum fluctuations of spacetime. Arguably it is the source of the holographic principle, which severely limits how densely information can be packed in space. Its physics is also intimately linked to that of black holes and computation. In particular, the same underlying physics is shown to govern the computational power of black hole quantum computers.

We review the early evolution of massive water Cherenkov tracking calorimeters, including the inception of the pioneering IMB and Dumand concepts and the two successor Kamiokande detectors. We also consider the ultimate facilities: a high-resolution megaton detector and the high-volume Antares detector plus its sequel, the Cubic Kilometer.

Paul Frampton played a seminal role in the scientific justification for the physics that drove IMB and its successors. We, the experimenters, pay tribute to Paul’s precocious support of searches for proton decay and neutrino oscillations. Led along the garden path for the first, we found the second, as well as the first (supernova) astrophysical neutrinos. This pays homage to Paul’s early days at Harvard and the decade that followed when he was a theory godfather to IMB and the detectors that followed. This includes Paul as the convener of the “Workshops on Grand Unification,” where, for example, was published the first paper to advocate IMB as a neutrino oscillation search with the baseline of the earth. All of us associated with IMB thank Paul immensely.

Most renormalizable quantum field theories can be rephrased in terms of Feynman diagrams that only contain dressed irreducible 2-, 3-, and 4-point vertices. These irreducible vertices in turn can be solved from equations that also only contain dressed irreducible vertices. The diagrams and equations that one ends up with do not contain any ultraviolet divergences. The original bare Lagrangian of the theory only enters in terms of freely adjustable integration constants. It is explained how the procedure proposed here is related to the renormalization group equations. The procedure requires the identification of unambiguous “paths” in a Feynman diagrams, and it is shown how to define such paths in most of the quantum field theories that are in use today. We do not claim to have a more convenient calculational scheme here, but rather a scheme that allows for a better conceptual understanding of ultraviolet infinities.

No abstract received.

Jet cross sections and shape variables in Z-decay to hadrons have a perturbative expansion in powers of the strong coupling α_s(M_Z). In addition non-perturbative effects suppressed by powers of Λ_QCD/M_Z contribute to these variables. In my talk, I reviewed how the non-perturbative contributions are calculated using the operator product expansion (OPE) and Soft-Collinear Effective field theory. Relations between the nonperturbative corrections to different shape variables were discussed.

Please refer to full text.

The appearance and interpretation of an accelerating universe may be an observed distortion resulting from a universe defined by spherical geometry. The annihilation of Planck and anti-Planck mass is paramount in explaining the Big-Bang [1]. In a model similar to the standard model of a Riemannian-Friedmann-Lemaitre hypersphere, the primordial energy of the Big-Bang is released in the form of electromagnetic-like radiation that expands radiantly in every 4D direction from time zero in the structure of hyper-waves carried by Planck and anti-Planck bosons. The resulting geometry shows that time is synonymous with the lightspeed expansion of our universe. In this model we find that time is not parallel but radiant. This implies that time is a vector - where every place we observe has a unique time direction (angle) with a magnitude (age) and a light cone. The result of this condition is the illusion that the further back we look from our position in spacetime, space appears to be contracted and time appears to run slower both exponentially and logarithmically. Simply stated, we can not rely on observations unless we understand the geometric distortions inherent in curved photon paths.

Theoretical progress on an approach to the Einstein-Schrodinger-Kursunoglu problem of EM – Gravity unification: the GEM (Gravity-Electro-Magnetism) theory, a combination of the Einstein-Sahkarov and Kaluza-Klein approaches, is summarized as well a collaborative hypothesis with the late Behram Kursunoglu concerning the Gamma Ray Bursters as “field unification events.” A derivation of the value of the Newton-Gravitation Constant, G, based on the splitting of both EM from gravity and electrons from protons with the appearance of the Kaluza-Klein fifth dimension in a U(1) symmetry, is presented. This results in the formula: G = e²/(4πε_om_pm_e) α exp( -2(m_p/m_e)^1/2) = 6.668 × 10^-11 newton-m²-kg^-2 where m_p and m_e are the proton and electron masses respectively and α is the fine structure constant. This value is within experimental uncertainty (1.5 parts per thousand) of the presently accepted value 6.673 × 10^-11 newton-m²-kg^-2. In the Newtonian limit the portion of the Kaluza-Klein action that is quadratic in first derivatives of the metric and in Poynting Flux appears in the form of a “Vacuum Bernoulli Equation” showing Gravitational energy density to be equated to an EM dynamic pressure that is quadratic in the local Poynting Flux: g²/(2π G) + S²/(c² L)= Constant, where g and S are the local gravity and Poynting vector magnitudes, respectively, and where L is the Lagrangian density of the EM field.

For uniform arrangements of magnetic fields, strings, or domain walls (together with the cosmological constant and non-relativistic matter), exact solutions to the Einstein equations are shown to lead to a universe with ellipsoidal expansion. We argue the results can be used to explain some features in the WMAP data. The magnetic field case is the easiest to motivate and has the highest possibility of yielding reliable constraints on observational cosmology.

We study the propagation of classical electromagnetic waves on the simplest four-dimensional spherically symmetric metric with a dilaton background field. Solutions to the relevant equations are obtained perturbatively in a parameter which measures the strength of the dilaton field (hence parameterizes the departure from Schwarzschild geometry). The loss of energy from outgoing modes is estimated as a back-scattering process against the dilaton background, which would affect the luminosity of stars with a dilaton field. The radiation emitted by a freely falling point-like source on such a background is also studied by numerical methods.

We study Big Crunch/Big Bang cosmologies that correspond to exact worldsheet superconformal field theories of type II strings. Generically, the Big Crunch fluctuation spectrum is altered when passing through the bounce singularity. The change in the spectrum is characterized by a function which is momentum and time-dependent. We compute this function explicitly and show that it indicates “entanglement entropy” with spacelike separated regions in the geometry. We demonstrate that in the Milne vacuum limit the fluctuation spectrum is unaltered as it passes through the singularity.

One of the goals of current cosmological studies is the determination of the expansion and acceleration rates of the universe as functions of redshift, and the determination of the properties of the dark energy that can explain these observations. Here the expansion and acceleration rates are determined directly from the data, without the need for the specification of a theory of gravity, and without adopting an a priori parameterization of the form or redshift evolution of the dark energy. We use the latest set of distances to SN standard candles from Riess et al. (2004), supplemented by data on radio galaxy standard ruler sizes, as described by Daly & Djorgovski (2003, 2004). We find that the universe transitions from acceleration to deceleration at a redshift of z_T ≈ 0.4, with the present value of q₀ = −0.35 ± 0.15. The standard “concordance model” with Ω₀ = 0.3 and Λ = 0.7 provides a reasonably good fit to the dimensionless expansion rate as a function of redshift, though it fits the dimensionless acceleration rate as a function of redshift less well. The expansion and acceleration rates are then combined with a theory of gravity to determine the pressure, energy density, and equation of state of the dark energy as functions of redshift. Adopting General Relativity as the correct theory of gravity, the redshift trends for the pressure, energy density, and equation of state of the dark energy out to z ~ 1 are determined, and are found to be generally consistent with the concordance model; they have zero redshift values of p₀ = −0.6 ± 0.15, f₀ = 0.62 ± 0.05, and w₀ = −0.9 ± 0.1.

Cluster observations provide unique and useful constraints on cosmological parameters. The contents of clusters and the rate of their formation are very sensitive to the mean matter density (Ω_M and the normalization and shape of the spectrum of initial density perturbations near the size scale of ~ 8h⁻¹ Mpc. Future and ongoing cluster studies constrain Ω_Λ (acceleration) and the equation of state of the “dark energy,” particularly in conjunction with either constraints from the cosmic microwave background or Type Ia supernovae of white dwarfs.

High energy cosmic ray experiments have identified an excess from the region of the Galactic Plane in a limited energy range around 10¹⁸ eV (EeV). This is very suggestive of neutrons as candidate primaries, because the directional signal requires relatively-stable neutral primaries, and time-dilated neutrons can reach Earth from typical Galactic distances when the neutron energy exceeds an EeV. We here point out that if the Galactic messengers are neutrons, then those with energies below an EeV will decay in flight, providing a flux of cosmic antineutrinos above a TeV which is observable at a kilometer-scale neutrino observatory. The expected event rate per year above 1 TeV in a detector such as IceCube, for example, is 20 antineutrino showers (all flavors) and a 1° directional signal of 4 events. A measurement of this flux can serve to identify the first extraterrestrial point source of TeV antineutrinos.

A field theory is proposed where the regular fermionic matter and the dark fermionic matter can be different states of the same “primordial” fermion fields. In regime of the fermion densities typical for normal particle physics, the primordial fermions split into three families identified with regular fermions. When fermion energy density becomes comparable with dark energy density, the theory allows transition to new type of states. The possibility of such Cosmo-Low Energy Physics (CLEP) states is demonstrated by means of solutions of the field theory equations describing FRW universe filled with homogeneous scalar field and uniformly distributed nonrelativistic neutrinos. Neutrinos in CLEP state are drawn into cosmological expansion by means of dynamically changing their own parameters. One of the features of the fermions in CLEP state is that in the late time universe their masses increase as a^3/2 (a = a(t) is the scale factor). The energy density of the cold dark matter consisting of neutrinos in CLEP state scales as a sort of dark energy; this cold dark matter possesses negative pressure and for the late time universe its equation of state approaches that of the cosmological constant. The total energy density of such universe is less than it would be in the universe free of fermionic matter at all.

The observed velocities of radio pulsars, which range in the hundreds kilometers per second, and many of which exceed 1000 km/s, are not explained by the standard physics of the supernova explosion. However, if a sterile neutrino with mass in the 1–20 keV range exists, it would be emitted asymmetrically from a cooling neutron star, which could give it a sufficient recoil to explain the pulsar motions. The same particle can be the cosmological dark mater. Future observations of X-ray telescopes and gravitational wave detectors can confirm or rule out this explanation.

No abstract received.

In this paper the mass of a universe, which began as a gravitationally closed, maximally spinning, Planck density quantum string is derived.

A universe beginning in such an initial state has been called a Super Spin Model universe. The total mass, M, of the Super Spin Model universe is shown to be a function of only four fundamental parameters ħ, c, G, e, such that: M = 4π²(ħc/G)^1/2 exp(ħc/e²).

The present paper primarily consists of a brief derivation of the above equation and a short synopsis of the Super Spin Model.

A scalar-tensor bimetric gravity model of early universe cosmology is reviewed. The metric frame with a variable speed of light (VSL) and a constant speed of gravitational waves is used to describe a Friedmann-Robertson-Walker universe. The Friedmann equations are solved for a radiation dominated equation of state and the power spectrum is predicted to be scale invariant with a scalar mode spectral index n_s = 0.97. The scalar modes are born in a ground state superhorizon and the fluctuation modes are causally connected by the VSL mechanism. The cosmological constant is equated to zero and there is no significant dependence on the scalar field potential energy. A possible way of distinguishing the bimetric gravity model from standard inflationary models is discussed.

Over the next decade or two, neutrino telescopes will map out the neutrino sky, analogous to the way the electromagnetic sky has been mapped for centuries. Like light and unlike cosmic-rays, the neutrinos will point back to their sources. Unlike light, the neutrinos are not attenuated at high energies and so will allow us to see farther into space, and deeper into sources. We illustrate with specific examples the promise which neutrino astronomy at energies from a TeV to a ZeV holds to study astrophysics and particle physics.

This paper gives an introduction to the MINOS experiment, discusses the ongoing construction of the NUMI beam line, and MINOS detectors and gives an update on their current status. The physics goals and expected sensitives are given for a nominal running period.

Search for ultra high-energy neutrino induced reactions, as part of a comprehensive probe of the neutrino sky and also investigation of the particle nature of the dark matter, with unique sensitivity to cold dark matter particles are described. We present a description of the design, scientific motivation and goals, performance and status of the IceCube experiment.

New experiments at accelerators and reactors are being designed to search for a possible non-zero value of the MNS matrix parameter θ₁₃.

Limits on the neutrino magnetic moment has been obtained by analyzing the energy spectrum distortions using 1496 days Super-Kamiokande-I solar neutrino data. A limit of μ_ν ≤ 3.6 × 10⁻¹⁰ μ_B at 90% C.L. has been obtained by fitting to the Super-Kamiokande day/night spectra. With additional information from other solar neutrino and KamLAND experiments constraining the oscillation region, a limit of μ_ν ≤ 1.1 × 10⁻¹⁰ μ_B at 90% C.L. was obtained.

The Sudbury Neutrino Observatory (SNO) is an underground heavy-water Cherenkov detector designed to detect ⁸B solar neutrinos through neutral (NC) and charged (CC) current interactions on deuterons and elastic scattering on electrons. The results from the pure D₂O phase of the experiment confirmed solar model predictions and gave strong evidence for flavor change. In the second phase, 2 tonnes of NaCl were added to the heavy water, in order to enhance the detection of neutral current interactions. This allowed for precision, energy-unconstrained measurements of the solar neutrino flux that exclude maximal flavor mixing at a level of 5σ. The talk will focus both on the characterization of the detector response and the implications of the results on Neutrino Oscillation Physics.

The present generation of measurements of the anomalous magnetic moment of the muon have reached sub part per million (ppm) precision, at which level they are not only sensitive to electromagnetic and hadronic interactions, but, for the first time, the electroweak interactions. Therefore comparing the experimental results with Standard Model evaluations provides stringent constraints on physics beyond our current model. From the latest measurements at Brookhaven National Laboratory, the anomalous magnetic moment is now known to within 0.5 ppm. These measurements have sparked much discussion in the physics community, as well as a re-examination of the theoretical evaluations of the anomaly. In 2001, measurements were made with negative muons that give a_μ− to 0.7 ppm. I describe the theory, experiment, and analysis techniques used to determine a_μ−.

Inelastic scattering using polarized nucleon targets and polarized charged lepton beams allows the extraction of the structure functions g₁ and g₂ which provide information on the spin structure of the nucleon. A program designed to study such processes has been underway in Jefferson Lab since 1998. A polarized electron beam, solid polarized NH₃ and ND₃ targets and the CEBAF Large Acceptance Spectrometer (CLAS) in Hall B were used to collect the desired data, 3 billion events were accumulated during the first run, and over 23 billion events were accumulated during the second run. The measurements cover the resonance region with unprecedented detail and add significantly to the DIS data set at low to moderate Q² and moderate to high x. The inclusive analysis of the data collected with beam energies of 1.6 GeV and 5.6 GeV has been mostly completed, yielding such important quantities as the photon nucleon asymmetry A₁, the spin structure function g₁, and its first moment Γ₁. These quantities allow us to study various aspects of the nucleon spin structure and to distinguish between different models of the valence spin structure. Measurements at low Q² are particularly interesting, as they shed light on the dynamics of transition from the partonic to hadronic degrees of freedom.

Super-Kamiokande’s measurements of the solar and atmospheric neutrino flux yielded first evidence for oscillation of atmospheric ν_μ’s into ν_τ’s and (together with data from the SNO experiment) first evidence for oscillation of solar ν_e’s into ν_μ’s or ν_τ’s. Data from Super-Kamiokande also constrained the neutrino mixing in both cases to be large. In Super-Kamiokande, the flux and energy spectrum of the first long baseline accelerator ν_μ’s were measured, they favor neutrino oscillations consistent with the atmospheric neutrino analysis.

Reactor experiments offer a promising way to determine θ₁₃ and are free from parameter degeneracies in neutrino oscillations, It is described how reactor measurements of sin² 2θ₁₃ can be improved by a near-far detector complex. The experimental lower bound is derived on the sensitivity to sin² 2θ₁₃ ≳ 0.02 based on the rate analysis, and an idea is given which may enable us to circumvent this bound. It is shown that in the Kashiwazaki-Kariwa plan (KASKA) the sensitivity to sin² 2θ₁₃ is approximately 0.02.

A minimal supersymmetric SO(10) model with one 10 and one 126 Higgs super-field predict all neutrino mixings as well as the solar mass difference squared in agreement with observations. However, the CKM CP phase is constrained to be in the second or third quadrant requiring a significant non-CKM component to CP violation to explain observations. We revisit this issue using type I and II seesaw formula for neutrino masses show that the addition of a nonrenormalizable term restores compatibility with neutrino data and CKM CP violation in both cases. We further find that the MSSM parameter tan β ≥ 30 in the type I model and lepton flavor violation and lepton electric dipole moments are accessible to proposed experiments in both type I and type II models. We also discuss the unification of the gauge couplings in type I model which requires an intermediate scale.

The seesaw theory, the leading theory for particle interactions, provides a viable mechanism for generating the matter-antimatter asymmetry of the universe. Testing the leptogenesis mechanism directly requires measurement of the d = 6 operator of the low-energy effective Lagrangian, in addition to the more familiar d = 5 operator which generates Majorana masses for the light neutrinos when the electroweak symmetry is spontaneously broken. This important experimental challenge awaits the next generation of particle physicists.

Astrophysical sources of ultrahigh energy neutrinos yield tau neutrino fluxes due to neutrino oscillations. We study in detail the contribution of tau neutrinos with energies above 10⁶ GeV relative to the contribution of the other flavors. We consider several different initial neutrino fluxes and include tau neutrino regeneration in transit through the Earth and energy loss of charged leptons. We discuss signals of tau neutrinos in detectors such as IceCube, RICE and ANITA.

We obtain the cross sections for the reactions where L is a massive lepton, i.e. a muon or a tau lepton. We do this from near threshold to relativistic energies. We further obtain the contributions of various form factors and interference terms to the cross section with a view to discovering if the contributions from hard to observe form factors such as the weak pseudoscalar form factor, F_P, and the weak electric form factor, F_E might be obtained via these reactions. The form factor F_E is particularly interesting as in the more usually observed p ↔ n transition it is a second class current and forbidden by G-parity. However in the p ↔ Λ transition it is not forbidden and it would be desirable to learn if it is present. Finally we discuss our results and prospects for these experiments.

In this talk I describe a natural framework for bi-large neutrino mixing within the context of two models – 1) a simple generalization of the MSSM and 2) an SO(10) model. Our starting point is the Frampton, Glashow, Yanagida [FGY] neutrino mass ansatz which can easily accomodate bi-large neutrino mixing. The main point of FGY, however, is to obtain a theory of neutrino masses with only one possible CP violating angle. They argue that the sign of the baryon asymmetry of the universe (assuming leptogenesis) is then correlated with CP asymmetries possibly observable in accelerator experiments. Unfortunately, there is a fly in the ointment. It was later shown by Raidal and Strumia [RS] that there is a sign ambiguity which frustrates the above correlation. We note that the Raidal-Strumia ambiguity is resolved in our models.

We relate the MNS and CKM mixing matrices using ideas from grand unification. We catalog models in terms of the family symmetries of the down quark mass matrices, and emphasize the role of the Cabibbo angle in the lepton mixing matrix. We find a large class of models with an observable CHOOZ angle .

We consider the radiative generation of a Chern-Simons addition to the effective action for a Lorentz-violating modification of electrodynamics. The coefficient of the induced Chern-Simons term is manifestly finite, but also potentially indeterminate. However, several values have been suggested as having special significance. We discuss two such special values, and it turns out that neither of them can be made consistent with the gauge invariance properties of the theory.

In this proceedings, I summarize two recently discovered theoretical implications that Lorentz violation has on physical systems. First, I discuss new models for neutrino oscillations in which relatively simple combinations of Lorentz-violating parameters can mimic the major features of the current neutrino oscillation data. Second, I will present results on Yang-Mills instantons in Lorentz-violating background fields. An explicit solution is presented for unit winding number in SU(2).

We discuss evolution of extended data sets in the framework of Nambu mechanics, a framework wherein time development is allowed a liberal interpretation in terms of dynamical generating functions.

We focus on D=11 supergravity as the low-energy limit of M-theory and pose the questions: (1) What are the $D=11$ symmetries? (2) How many supersymmetries can M-theory vacua preserve?

The gauge/string-gravity duality correspondence opened renewed hope and possibility to address some of the fundamental and non-perturbative QCD problems of in particle physics, such as hadron spectrum and Regge behavior of the scattering amplitude at high energies. One of the most fundamental and long-standing problems is the high energy behavior of the total cross-sections. According to a series of exhaustive tests by the COMPETE group, (1) total cross sections have a universal Heisenberg behavior in energy corresponding to the maximal energy behavior allowed by the Froissart bound, i.e., A + B In²(s/s₀) with B ~ 0.32 mb and s₀ ~ 34.41 GeV² for all reactions, and (2). the factorization relation among σ_pp,even, σ_γp and σ_γγ is well satisfied by experiments. I discuss the recent interesting application of the gauge/string-gravity duality of AdS/CFT correspondence with a deformed background metric so as to break the conformal symmetry that lead to the Heisenberg behavior of rising total cross sections, and present some preliminary results on the high energy QCD from Planckian scattering in AdS and black-hole production.

Many theoretical approaches to quantum gravity predict the breakdown of Lorentz symmetry at Planck energies. Kinematical cosmic-ray studies are a sensitive tool in the search for such effects. This talk discusses the construction of test dispersion relations for such analyses.

This is Generalized holonomy.

A brief review of recent developments on soft breaking in SUSY, string and intersecting D brane models is given. The constraints on soft breaking parameters from WMAP data are discussed. A discussion of the constraints of modular invariance on soft breaking within heterotic string models is given. It is shown that the radiative electroweak symmetry breaking leads to a more stringent constraint on soft parameters here than in SUGRA models. Finally, a brief review of recent developments on soft breaking in the framework of intersecting D brane models is given. The issue of gauge coupling unification within intersecting D brane models is briefly discussed.

Recently, Diaconescu, Moore and Witten provided a nontrivial link between K-theory and M-theory, by deriving the partition function of the Ramond-Ramond fields of Type IIA string theory from an E8 gauge theory in eleven dimensions. We give some relations between twisted K-theory and M-theory by adapting the method of Diaconescu-Moore-Witten and Moore-Saulina. In particular, we construct the twisted K-theory torus which defines the partition function, and also discuss the problem from the E8 loop group picture, in which the Dixmier-Douady class is the Neveu-Schwarz field. In the process of doing this, we encounter some mathematics that is new to the physics literature. In particular, the eta differential form, which is the generalization of the eta invariant, arises naturally in this context. We conclude with several open problems in mathematics and string theory.

As a prelude to the standard model in curved space time, we present a model of a left- and a right- chiral field living on a two-sheeted space-time. The resulting action functionals include novel interactions due to extended gravity.

No abstract received.

No abstract received.

Talk presented at the 2003 Coral Gables conference in honor and appreciation of the work of Professor Behram Kursunoglu, general relativist extraordinaire and founder of the Coral Gables series of conferences, whose untimely death occurred shortly before the 2003 conference.

No abstract received.

Some reminiscences on the life of Professor Behram Kursunoglu and his family.