abstract

Interpreting intermittency as the result of a cascade through a random medium, it is shown that the long time behaviour of the \(D\)-dimensional random heat equation generates intermittent patterns as well as a multifractal structure. Intermittent fluctuations are arranged in a hierarchical fashion. Moreover, multifractal analysis reveals that the cascading system organizes itself into a point-like set of “spikes” whose statistical properties are given. Such “spikes” are similar to localized asymptotic states. This allows one to sketch out possible applications to “non-thermal” transitions in multiparticle production.

abstract

We discuss the phenomenology of point matter distributions, using examples of photoelectron count arrival times, galaxy distributions and multihadron production at high energies. Count distributions in phase space cells, multiplicity moments and correlation functions are discussed along with their interconnections. The possible description of higher order cumulant correlations (both for hadrons and galaxies) by linked two-particle cumulants and negative binomial coefficients, is reviewed.

abstract

From all orbits described by a ball bouncing elastically inside a tri-angular billiard some special classes are selected for further numerical investigation. One of these classes consists of all orbits starting in a direction perpendicular to a side. Evidence is presented to show that almost all orbits of this kind are either periodic or end in a corner. The starting points with the same period form intervals, which are distributed in some regular fashion. Even for orbits with very high period the phase portrait and the velocity portrait show peculiar regularities. Although these observations suggest a number of theorems with general validity, the author cannot support them with more than plausibility arguments.

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We discuss the general structure of relativistic theories in 2+1 dimensions whose physical states carry fractional spin and statistics at both the first-quantized and second-quantized level. We show that the Poincaré representations carried by the physical states of the theory are modified by coupling the particle-number current to a topological term. We discuss the spin-statistics theorem and the dependence of the total angular momentum on the number of particles and we show that due to short-distance divergencies they are different in the first- and second-quantized theories.

abstract

The gauge structure, both abelian and nonabelian, induced in strong interaction processes is discussed in this lecture. First a simple quantum mechanical system is analysed, followed by an extension, via chiral bag model, to a more realistic hadronic system. The resulting induced gauge potential, widely known as Berry potential, is then shown to describe excited states of nonstrange baryons and ground states of strange and charmed baryons. Geometric phases that emerge in such processes are relevant for spin-isospin transmutation, hyperfine splittings in the spectrum and render the skyrmion description also applicable to massive-quark baryons, exhibiting in the massive-quark limit the “Wisgur” symmetry that arises from QCD. It is proposed that the induced gauge structure underlies all low-energy properties of QCD in the nonperturbative regime.

abstract

In this talk we discuss how to use effective chiral Lagrangians to investigate in some detail Chanowits’s “no lose corollary”. That is, we will assume that electroweak symmetry breaking occurs through an unknown strong interaction that, however, produces no resonances in the energy region that will be probed by a \(pp\) supercollider like the SSC. We find that if an enhancement in the yield of V\(_{\rm L}\)V\(_{\rm L}\) pairs is observed, it will be very difficult to relate it to an underlying theory. We also find that in a “worse case scenario” this enhancement might not be sufficiently large for detection at the SSC.

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The saturation properties of nuclear matter axe dominated by the dynamics of a self-consistent treatment of correlations and the structure of the Dirac spinors of the nucleons in the medium. It is demonstrated that ground-state properties of finite nuclei are furthermore sensitive to the range of the interaction. This yields different compressibilities for infinite matter and finite nuclei. The medium dependence of the effective mass of nucleons and mesons axe studied within the model of Nambu and Jona–Lasinio. A possible connection of this model to QCD is discussed.

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We show that non-perturbative contributions to the nucleon matrix elements of quark and gluon operators may explain the surprising experimental results of the EMC Collaboration on the nucleon’s axial charge. We discuss the phenomenological consequences of this way of understanding the data, and we argue that recent experimental results on the Gottfried sum rule may be understood in the same way.

abstract

The diquark model for exclusive reactions at moderately large momentum transfer is reviewed. This model is a modification of the Brodsky–Lepage picture in which diquarks are considered as quasi-elementary constituents of baryons. Recent applications of this model are discussed: weak and electromagnetic formfactors of baryons, Compton scattering, photoproduction of mesons and \(p\bar p\) annihilations into pairs of heavy flavour hadrons.

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We briefly review the parton model and give reasons why an accurate determination of the parton distributions is important. We summarize the recent determinations of the parton distributions of the proton and describe the role played by deep inelastic lepton–nucleon scattering and related data. We compare the determination of \(\alpha _{\rm s}(M_Z)\) from deep inelastic scattering with the average of the LEP measurements. We use a simple model to illustrate why the Lipatov equation predicts a small \(x\) behaviour of the gluon distribution of the form \(xg \sim x^{-\lambda }\) with \(\lambda \simeq 0.5\). We describe how shadowing contributions suppress this singular behaviour and we discuss a structure function analysis which incorporates these effects at small \(x\). We introduce the GLR equation and outline how an explicit numerical solution has been obtained for the behaviour of the gluon distribution at small \(x\). We mention various future experimental probes of the small \(x\) region.

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We discuss the possibility that the Nolen–Schiffer anomaly, an old problem in nuclear physics, might be a signal that the neutron–proton mass difference is smaller in nuclei than in vacuum.