Euclidean Approach to the Entropy for a Scalar Field in Rindler-like Space-Times

The off-shell entropy for a massless scalar field in a D-dimensional Rindler-like space-time is investigated within the conical Euclidean approach in the manifold C_\be\times\M^N, C_\be being the 2-dimensional cone, making use of the zeta-function regularisation. Due to the presence of conical singularities, it is shown that the relation between the zeta-function and the heat kernel is non trivial and, as first pointed out by Cheeger, requires a separation between small and large eigenvalues of the Laplace operator. As a consequence, in the massless case, the (naive) non existence of the Mellin transform is by-passed by the Cheeger's analytical continuation of the zeta-function on manifold with conical singularities. Furthermore, the continuous spectrum leads to the introduction of smeared traces. In general, it is pointed out that the presence of the divergences may depend on the smearing function and they arise in removing the smearing cutoff. With a simple choice of the smearing function, horizon divergences in the thermodynamical quantities are recovered and these are similar to the divergences found by means of off-shell methods like the brick wall model, the optical conformal transformation techniques or the canonical path integral method.Comment: 17 pages, LaTex. A sign error corrected and few comments adde

Oralism: a sign of the times? The contest for deaf communication in education provision in late nineteenth-century Scotland

Disability history is a diverse field. In focussing upon children within deaf education in late nineteenth-century Scotland, this essay reflects some of that diversity. In 1880, the International Congress on the Education of the Deaf in Milan stipulated that speech should have ‘preference’ over signs in the education of deaf children. The mode of achieving this, however, effectively banned sign language. Endeavours to teach deaf children to articulate were not new, but this decision placed pressures on deaf institutions to favour the oral system of deaf communication over other methods. In Scotland efforts were made to adopt oralism, and yet educators were faced with the reality that this was not good educational practice for most pupils. This article will consider responses of Scottish educators of deaf children from the 1870s until the beginning of the twentieth century

Measurement of W Polarisation at LEP

The three different helicity states of W bosons produced in the reaction e+ e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation

Search for Anomalous Couplings in the Higgs Sector at LEP

Anomalous couplings of the Higgs boson are searched for through the processes e^+ e^- -> H gamma, e^+ e^- -> e^+ e^- H and e^+ e^- -> HZ. The mass range 70 GeV < m_H < 190 GeV is explored using 602 pb^-1 of integrated luminosity collected with the L3 detector at LEP at centre-of-mass energies sqrt(s)=189-209 GeV. The Higgs decay channels H -> ffbar, H -> gamma gamma, H -> Z\gamma and H -> WW^(*) are considered and no evidence is found for anomalous Higgs production or decay. Limits on the anomalous couplings d, db, Delta(g1z), Delta(kappa_gamma) and xi^2 are derived as well as limits on the H -> gamma gamma and H -> Z gamma decay rates

Measurement of W Polarisation at LEP

The three different helicity states of W bosons produced in the reaction e+ e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation

Z Boson Pair-Production at LEP

Events stemming from the pair-production of Z bosons in e^+e^- collisions are studied using 217.4 pb^-1 of data collected with the L3 detector at centre-of-mass energies from 200 GeV up to 209 GeV. The special case of events with b quarks is also investigated. Combining these events with those collected at lower centre-of-mass energies, the Standard Model predictions for the production mechanism are verified. In addition, limits are set on anomalous couplings of neutral gauge bosons and on effects of extra space dimensions

Bose-Einstein Correlations of Neutral and Charged Pions in Hadronic Z Decays

Bose-Einstein correlations of both neutral and like-sign charged pion pairs are measured in a sample of 2 million hadronic Z decays collected with the L3 detector at LEP. The analysis is performed in the four-momentum difference range 300 MeV < Q < 2 GeV. The radius of the neutral pion source is found to be smaller than that of charged pions. This result is in qualitative agreement with the string fragmentation model

Measurement of Exclusive rho+rho- Production in Mid-Virtuality Two-Photon Interactions and Study of the gamma gamma* -> rho rho Process at LEP

Exclusive rho+rho- production in two-photon collisions between a quasi-real photon, gamma, and a mid-virtuality photon, gamma*, is studied with data collected at LEP at centre-of-mass energies root(s)=183-209GeV with a total integrated luminosity of 684.8pb^-1. The cross section of the gamma gamma* -> rho+ rho- process is determined as a function of the photon virtuality, Q^2, and the two-photon centre-of-mass energy, W_gg, in the kinematic region: 0.2GeV^2 < Q^2 <0.85GeV^2 and 1.1GeV < W_gg < 3GeV. These results, together with previous L3 measurements of rho0 rho0 and rho+ rho- production, allow a study of the gamma gamma* -> rho rho process over the Q^2-region 0.2GeV^2 < Q^2 < 30 GeV^2

Neutral-Current Four-Fermion Production in e+e- Interactions at LEP

Neutral-current four-fermion production, e+e- -> ffff is studied in 0.7/fb of data collected with the L3 detector at LEP at centre-of-mass energies root(s)=183-209GeV. Four final states are considered: qqvv, qqll, llll and llvv, where l denotes either an electron or a muon. Their cross sections are measured and found to agree with the Standard Model predictions. In addition, the e+e- -> Zgamma* -> ffff process is studied and its total cross section at the average centre-of-mass energy 196.6GeV is found to be 0.29 +/- 0.05 +/- 0.03 pb, where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model prediction of 0.22 pb. Finally, the mass spectra of the qqll final states are analysed to search for the possible production of a new neutral heavy particle, for which no evidence is found

Measurement of the Running of the Electromagnetic Coupling at Large Momentum-Transfer at LEP

The evolution of the electromagnetic coupling, alpha, in the momentum-transfer range 1800GeV^2 < -Q^2 < 21600GeV^2 is studied with about 40000 Bhabha-scattering events collected with the L3 detector at LEP at centre-of-mass energies 189-209GeV. The running of alpha is parametrised as: alpha(Q^2) = alpha_0/(1-C Delta alpha(Q^2)), where alpha_0=\alpha(Q^2=0) is the fine-structure constant and C=1 corresponds to the evolution expected in QED. A fit to the differential cross section of the e+e- ->e+e- process for scattering angles in the range |cos theta|<0.9 excludes the hypothesis of a constant value of alpha, C=0, and validates the QED prediction with the result: C = 1.05 +/- 0.07 +/- 0.14, where the first uncertainty is statistical and the second systematic