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

The Information Geometry of the Ising Model on Planar Random Graphs

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the case where there are two such parameters -- such as the Ising model with inverse temperature $\beta$ and external field $h$. In various two parameter calculable models the scalar curvature ${\cal R}$ of the information metric has been found to diverge at the phase transition point $\beta_c$ and a plausible scaling relation postulated: ${\cal R} \sim |\beta- \beta_c|^{\alpha - 2}$. For spin models the necessity of calculating in non-zero field has limited analytic consideration to 1D, mean-field and Bethe lattice Ising models. In this letter we use the solution in field of the Ising model on an ensemble of planar random graphs (where $\alpha=-1, \beta=1/2, \gamma=2$) to evaluate the scaling behaviour of the scalar curvature, and find ${\cal R} \sim | \beta- \beta_c |^{-2}$. The apparent discrepancy is traced back to the effect of a negative $\alpha$.Comment: Version accepted for publication in PRE, revtex

Renormalization of composite operators

The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel transport of the operators along the RG trajectory. The connection on this one-dimensional manifold governs the scale evolution of the operator mixing. It is shown that the solution of the eigenvalue problem of the connection gives the various scaling regimes and the relevant operators there. The relation to perturbative renormalization is also discussed in the framework of the $\phi^3$ theory in dimension $d=6$.Comment: 24 pages, revtex (accepted by Phys. Rev. D), changes in introduction and summar

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

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

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

First limits on the 3-200 keV X-ray spectrum of the quiet Sun using RHESSI

We present the first results using the Reuven Ramaty High-Energy Solar Spectroscopic Imager, RHESSI, to observe solar X-ray emission not associated with active regions, sunspots or flares (the quiet Sun). Using a newly developed chopping technique (fan-beam modulation) during seven periods of offpointing between June 2005 to October 2006, we obtained upper limits over 3-200 keV for the quietest times when the GOES12 1-8A flux fell below $10^{-8}$ Wm$^{-2}$. These values are smaller than previous limits in the 17-120 keV range and extend them to both lower and higher energies. The limit in 3-6 keV is consistent with a coronal temperature $\leq 6$ MK. For quiet Sun periods when the GOES12 1-8A background flux was between $10^{-8}$ Wm$^{-2}$ and $10^{-7}$ Wm$^{-2}$, the RHESSI 3-6 keV flux correlates to this as a power-law, with an index of $1.08 \pm 0.13$. The power-law correlation for microflares has a steeper index of $1.29 \pm 0.06$. We also discuss the possibility of observing quiet Sun X-rays due to solar axions and use the RHESSI quiet Sun limits to estimate the axion-to-photon coupling constant for two different axion emission scenarios.Comment: 4 pages, 3 figures, Accepted by ApJ letter

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

Renormalization of modular invariant Coulomb gas and Sine-Gordon theories, and quantum Hall flow diagram

Using the renormalisation group (RG) we study two dimensional electromagnetic coulomb gas and extended Sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following proposal for a SL(2,Z) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram.Comment: 10 pages, 1 EPS figure include