Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.Comment: 34 pages, v2 contains minor corrections to the published versio

On the "Universal" Quantum Area Spectrum

There has been much debate over the form of the quantum area spectrum for a black hole horizon, with the evenly spaced conception of Bekenstein having featured prominently in the discourse. In this letter, we refine a very recently proposed method for calibrating the Bekenstein form of the spectrum. Our refined treatment predicts, as did its predecessor, a uniform spacing between adjacent spectral levels of $8\pi$ in Planck units; notably, an outcome that already has a pedigree as a proposed ``universal'' value for this intrinsically quantum-gravitational measure. Although the two approaches are somewhat similar in logic and quite agreeable in outcome, we argue that our version is conceptually more elegant and formally simpler than its precursor. Moreover, our rendition is able to circumvent a couple of previously unnoticed technical issues and, as an added bonus, translates to generic theories of gravity in a very direct manner.Comment: 7 Pages; (v2) now 9 full pages, significant changes to the text and material added but the general theme and conclusions are unchange

Quantum fluctuations of the electroweak sphaleron: Erratum and Addendum

We correct an error in our treatment of the tadpole contribution to the fluctuation determinant of the sphaleron, and also a minor mistake in a previous estimate. Thereby the overall agreement between the two existing exact computations and their consistency with the estimate is improved considerably.Comment: 4 pages, Dortmund preprint DO-TH-93/19E

A projective Dirac operator on CP^2 within fuzzy geometry

We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz is suitable for noncommutative generalisation within the framework of fuzzy geometry. Along the way we identify the physical spinors and construct the canonical spin_c bundle in this formulation. The chirality operator is also given in two equivalent forms. Finally, using representation theory we obtain the eigenspinors and calculate the full spectrum. We use an argument from the fuzzy complex projective space CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show that our commutative projected spin_c bundle has the correct SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos correcte

The Information Geometry of the One-Dimensional Potts Model

In various statistical-mechanical models the introduction of a metric onto the space of parameters (e.g. the temperature variable, $\beta$, and the external field variable, $h$, in the case of spin models) gives an alternative perspective on the phase structure. For the one-dimensional Ising model the scalar curvature, ${\cal R}$, of this metric can be calculated explicitly in the thermodynamic limit and is found to be ${\cal R} = 1 + \cosh (h) / \sqrt{\sinh^2 (h) + \exp (- 4 \beta)}$. This is positive definite and, for physical fields and temperatures, diverges only at the zero-temperature, zero-field ``critical point'' of the model. In this note we calculate ${\cal R}$ for the one-dimensional $q$-state Potts model, finding an expression of the form ${\cal R} = A(q,\beta,h) + B (q,\beta,h)/\sqrt{\eta(q,\beta,h)}$, where $\eta(q,\beta,h)$ is the Potts analogue of $\sinh^2 (h) + \exp (- 4 \beta)$. This is no longer positive definite, but once again it diverges only at the critical point in the space of real parameters. We remark, however, that a naive analytic continuation to complex field reveals a further divergence in the Ising and Potts curvatures at the Lee-Yang edge.Comment: 9 pages + 4 eps figure

Polarised infrared emission from X-ray binary jets

Near-infrared (NIR) and optical polarimetric observations of a selection of X-ray binaries are presented. The targets were observed using the Very Large Telescope and the United Kingdom Infrared Telescope. We detect a significant level (3 sigma) of linear polarisation in four sources. The polarisation is found to be intrinsic (at the > 3 sigma level) in two sources; GRO J1655-40 (~ 4-7% in H and Ks-bands during an outburst) and Sco X-1 (~ 0.1-0.9% in H and K), which is stronger at lower frequencies. This is likely to be the signature of optically thin synchrotron emission from the collimated jets in these systems, whose presence indicates a partially-ordered magnetic field is present at the inner regions of the jets. In Sco X-1 the intrinsic polarisation is variable (and sometimes absent) in the H and K-bands. In the J-band (i.e. at higher frequencies) the polarisation is not significantly variable and is consistent with an interstellar origin. The optical light from GX 339-4 is also polarised, but at a level and position angle consistent with scattering by interstellar dust. The other polarised source is SS 433, which has a low level (0.5-0.8%) of J-band polarisation, likely due to local scattering. The NIR counterparts of GRO J0422+32, XTE J1118+480, 4U 0614+09 and Aql X-1 (which were all in or near quiescence) have a linear polarisation level of < 16% (3 sigma upper limit, some are < 6%). We discuss how such observations may be used to constrain the ordering of the magnetic field close to the base of the jet in such systems.Comment: Accepted to be published in MNRAS; 13 pages, 6 figure

Contextual novelty changes reward representations in the striatum

Reward representation in ventral striatum is boosted by perceptual novelty, although the mechanism of this effect remains elusive. Animal studies indicate a functional loop (Lisman and Grace, 2005) that includes hippocampus, ventral striatum, and midbrain as being important in regulating salience attribution within the context of novel stimuli. According to this model, reward responses in ventral striatum or midbrain should be enhanced in the context of novelty even if reward and novelty constitute unrelated, independent events. Using fMRI, we show that trials with reward-predictive cues and subsequent outcomes elicit higher responses in the striatum if preceded by an unrelated novel picture, indicating that reward representation is enhanced in the context of novelty. Notably, this effect was observed solely when reward occurrence, and hence reward-related salience, was low. These findings support a view that contextual novelty enhances neural responses underlying reward representation in the striatum and concur with the effects of novelty processing as predicted by the model of Lisman and Grace (2005)

Study of thermal protection requirements for a lifting body entry vehicle suitable for near-earth missions Final report

Reentry and abort trajectory analyses, and thermal protection requirements for lifting body entry vehicle

Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory

A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations are found. These include generalisations of those found by Flato and Fronsdal for SO(3,2). In even dimensions the products for free representations split into two types depending on whether the dimension is divisible by four or not.Comment: 43 pages, uses harvmac,version 2 2 references added, minor typos correcte