International Journal of Modern Physics A

We have made a systematic study of the electric dipole moment (EDM) of neutron D_n in various models of CP violation.

We find that

(i) in the standard KM model with 3 families, the neutron EDM is in the range 1.4 × 10⁻³³ ≤ |D_n| ≤ 1.6 × 10⁻³¹e.cm,

(ii) the two Higgs doublet model has approximately the same value of D_n as the standard model,

(iii) D_n in the Weinberg model is predicted to satisfy |D_n| > 10⁻²⁵e.cm,

(iv) in a class of left-right symmetric models D_n is of the order of 10^−26±1e.cm,

(v) in supersymmetric models, D_n is of order 10⁻²²ϕ e.cm with ϕ being the possible phase difference of gluino mass and the gluino-quark-squark mixing matrix,

(vi)the strong CP parameter θ is found to be θ < 10⁻⁹, using the present experimental limit that |D_n| < 2.6 × 10⁻²⁵e.cm with 90% confidence.

We review in this paper the first results obtained in an attempt at understanding quantum space-time based on a new extension of the principle of relativity and on the geometrical concept of fractals. We present methods for dealing with the nondifferentiability and the infinities of fractals, as a first step towards the definition and intrinsic description of a fractal space. After having recalled that the Heisenberg relations imply a transition of spatial coordinates of a particle to fractal dimension 2 about the de Broglie length λ = ħ/p, it is suggested that a similar transition occurs for temporal coordinates about the de Broglie time τ = ħ/E. We then investigate the hypothesis that the microstructure of space-time is of fractal nature, and that the observed properties of the quantum world at a given resolution result from the smoothing of curvilinear coordinates of such a spacetime projected into classical spacetime. Along this road, we successively study the link of fractal dimension 2 to spin, we give first hints on the expected behavior of families of fractal geodesics, and we exhibit a general class of fractal structures which is assumed to yield a lowest order description of the quantum vacuum. The links between the new approach and both special and general relativity are touched upon. We finally suggest that the anomalous peaks recently observed in the spectra of positrons from supercritical heavy ion collisions may be understood in this context.

Gravitational Bags are spherically symmetric solutions of higher-dimensional Kaluza Klein (K – K) theories, where the compact dimensions become very large near the center of the geometry, although they are small elsewhere. The K – K excitations therefore become very light when located near the center of this geometry and this appears to affect drastically the naive tower of the masses spectrum of K – K theories. In the context of string theories, string excitations can be enclosed by Gravitational Bags, making them not only lighter, but also localized, as observed by somebody, that does not probe the central regions. Strings, however, can still have divergent sizes, as quantum mechanics seems to demand, since the extra dimensions blow up at the center of the geometry. From a projected 4-D point of view, very massive string bits may lie inside their Schwarzschild radii, as pointed out by Casher, Gravitational Bags however are horizon free objects, so no conflict with macroscopic causality arises if the string excitations are enclosed by Gravitational Bags.

We discuss unitary realizations of the Heisenberg group and the linear canonical transformations over a complex Hilbert space but with dynamical variables on a p-adic field Q_p. For all p, an appropriate choice of phase turns the realization of the linear canonical transformation into a representation up to a sign of SL(2, Q_p). We give the spectra of the subgroups corresponding to the free particle and the harmonic oscillator. We discuss briefly the possibility of an adelic interpretation.

Orbifold compactifications of open and closed bosonic strings are examined and constrained by unitarity requirements. In particular, the role of crosscap and boundary states in evaluating amplitudes is investigated.

We introduce variational forms, which are generalizations of Cartan's forms,¹ and investigate 2-dimensional R²-gravity using them.

By performing the BRST quantization for the Type II Green-Schwarz string with the truncated κ-symmetry recently proposed by Kallosh and Rahmanov, we confirm that the quadratic ghost interaction is indeed sufficient for the unitarity of the theory. The analysis of the cancellation of the conformal anomaly gives the correct critical dimension.

The gauge dependence of the effective action of composite fields is investigated. The Ward identities for general gauge theories with arbitrary composite fields are found. It is proved that the extremum of the action of composite fields does not depend on the gauge condition. An example of the calculation of the effective action of composite fields in Yang-Mills theory is discussed.

We consider in the framework of the Brodsky-Farrar-Lepage scheme allowing for (scalar) diquarks as quasi-elementary constituents. We compute the unpolarized cross section using different proton wave functions. Their normalization is fixed by computing the electromagnetic form factor of the proton in the same framework. Good agreement with the experimental data can be obtained. Two-photon annihilation into other baryons is also discussed.

A method of relating infinite dimensional Lie algebras to basis dependent sequences of finite dimensional Lie algebras is introduced. Diff_A S² and Diff_A T² are shown to be N → ∞ limits of SU(N), with a limiting procedure, and "SU(∞)'s", that differ from the usual Kac Moody ones. After a detailed presentation of these two 'principal' examples, the general construction is outlined, which seems to work for the Poisson algebra of more or less any homogenous symplectic manifold.

We have investigated photonuclear reactions in ²⁰⁸Pb from the reaction threshold to pion production threshold. In the Giant Dipole Resonance energy region we have considered the results of a recent 1⁻ 1p-1h continuum calculation and multiplied them, heuristically, by a factor, which includes the effect of neglected nucleon-nucleon correlations, through the occupation number probabilities of the single particle and hole energy levels. We have thus obtained a much better agreement with experiment. In the energy region above the Giant Dipole Resonance we have considered a quasi deuteron model, which contains the effect of nucleon swelling. Both this model and corresponding integrated sum rules yield a satisfactory agreement with experiment.

The physical subspace of the SL(2, R) current algebra based model of induced 2d gravity is investigated. Using an appropriate ground state, an equation guaranteeing the non-negativity of this subspace is derived using a BRS analysis. In case of the ground state allowing the derivation of simple differential equations for the correlation functions the presence of an SL(2, R) background charge is exhibited. It is shown that changing one ground state for the other converts the KPZ equation for the anomalous dimensions to the previous equation for physical states.

Due to chiral supersymmetry the (nonzero mode) spectral and symmetry properties of a 4-dimensional, self-dual Dirac-Yang-Mills operator can be recovered from those of the corresponding scalar Laplacian D². It is shown that a similar result holds for higher spins, and that in the 4-vector case the supersymmetric partners are − D²1₄ and the fluctuation operator. The reduction to D² is used to simplify previous analyses of the (nonzero mode) spectrum of and of the fluctuations for a BPS-monopole, and to explain the Kepler and su(2/2) (super)symmetries of a system studied recently by D'Hoker and Vinet.

1635 fragments of charge two from 2550 ¹²C-Em interactions at 4.5 A GeV/c have been used to study the dependence of mean free path on the distance from the point of their emission. No evidence is found for the anomalously short mean free path in the first few centimeters of the point of emission.

Bosonic string scattering amplitudes on the disc and the projective plane are compared with amplitudes from the effective field theory derived by demanding consistency of string propagation in background massless fields. Path integral (as opposed to BRST) quantization is used throughout, with the ghost fields integrated out. We point out a difficulty in defining a covariant dilaton vertex operator in this formalism. A nonstandard graviton vertex operator is constructed, by which we compute the vacuum energy for the two topologies and find that it has the correct ratio to the dilaton tadpole, as predicted by the effective Lagrangian. Factorization of tadpole divergences in N-point amplitudes leads to the same result, modulo a paradox discovered by Fischler, Klebanov, and Susskind, which is reviewed. We also show that the dilaton two- and three-point functions agree with the exponential form of the dilaton potential in the effective action, despite quadratic divergences that initially appear in these amplitudes.