Fermion Determinants

The current status of bounds on and limits of fermion determinants in two, three and four dimensions in QED and QCD is reviewed. A new lower bound on the two-dimensional QED determinant is derived. An outline of the demonstration of the continuity of this determinant at zero mass when the background magnetic field flux is zero is also given.Comment: 10 page

Euler-Heisenberg lagrangians and asymptotic analysis in 1+1 QED, part 1: Two-loop

We continue an effort to obtain information on the QED perturbation series at high loop orders, and particularly on the issue of large cancellations inside gauge invariant classes of graphs, using the example of the l - loop N - photon amplitudes in the limit of large photons numbers and low photon energies. As was previously shown, high-order information on these amplitudes can be obtained from a nonperturbative formula, due to Affleck et al., for the imaginary part of the QED effective lagrangian in a constant field. The procedure uses Borel analysis and leads, under some plausible assumptions, to a number of nontrivial predictions already at the three-loop level. Their direct verification would require a calculation of this `Euler-Heisenberg lagrangian' at three-loops, which seems presently out of reach. Motivated by previous work by Dunne and Krasnansky on Euler-Heisenberg lagrangians in various dimensions, in the present work we initiate a new line of attack on this problem by deriving and proving the analogous predictions in the simpler setting of 1+1 dimensional QED. In the first part of this series, we obtain a generalization of the formula of Affleck et al. to this case, and show that, for both Scalar and Spinor QED, it correctly predicts the leading asymptotic behaviour of the weak field expansion coefficients of the two loop Euler-Heisenberg lagrangians.Comment: 28 pages, 1 figures, final published version (minor modifications, refs. added

The SCUBA Local Universe Galaxy Survey I: First Measurements of the Submillimetre Luminosity and Dust Mass Functions

We have used SCUBA to observe a complete sample of 104 galaxies selected at 60 microns from the IRAS BGS and we present here the 850 micron measurements. Fitting the 60,100 and 850 micron fluxes with a single temperature dust model gives the sample mean temperature T=36 K and beta = 1.3. We do not rule out the possibility of dust which is colder than this, if a 20 K component was present then our dust masses would increase by factor 1.5-3. We present the first measurements of the luminosity and dust mass functions, which were well fitted by Schechter functions (unlike those 60 microns). We have correlated many global galaxy properties with the submillimetre and find that there is a tendancy for less optically luminous galaxies to contain warmer dust and have greater star formation efficiencies (cf. Young 1999). The average gas-to-dust ratio for the sample is 581 +/- 43 (using both atomic and molecular hydrogen), significantly higher than the Galactic value of 160. We believe this discrepancy is due to a cold dust component at T < 20 K. There is a suprisingly tight correlation between dust mass and the mass of molecular hydrogen as estimated from CO measurements, with an intrinsic scatter of ~50%.Comment: 24 pages, 15 figures, 8 tables, accepted for publication in MNRA

Rapid coastal deoxygenation due to ocean circulation shift in the NW Atlantic.

Global observations show that the ocean lost approximately 2% of its oxygen inventory over the last five decades 1-3, with important implications for marine ecosystems 4, 5. The rate of change varies with northwest Atlantic coastal waters showing a long-term drop 6, 7 that vastly outpaces the global and North Atlantic basin mean deoxygenation rates 5, 8. However, past work has been unable to resolve mechanisms of large-scale climate forcing from local processes. Here, we use hydrographic evidence to show a Labrador Current retreat is playing a key role in the deoxygenation on the northwest Atlantic shelf. A high-resolution global coupled climate-biogeochemistry model 9 reproduces the observed decline of saturation oxygen concentrations in the region, driven by a retreat of the equatorward-flowing Labrador Current and an associated shift toward more oxygen-poor subtropical waters on the shelf. The dynamical changes underlying the shift in shelf water properties are correlated with a slowdown in the simulated Atlantic Meridional Overturning Circulation 10. Our results provide strong evidence that a major, centennial-scale change of the Labrador Current is underway, and highlight the potential for ocean dynamics to impact coastal deoxygenation over the coming century

Chern-Simons matrix model: coherent states and relation to Laughlin wavefunctions

Using a coherent state representation we derive many-body probability distributions and wavefunctions for the Chern-Simons matrix model proposed by Polychronakos and compare them to the Laughlin ones. We analyze two different coherent state representations, corresponding to different choices for electron coordinate bases. In both cases we find that the resulting probability distributions do not quite agree with the Laughlin ones. There is agreement on the long distance behavior, but the short distance behavior is different.Comment: 15 pages, LaTeX; one reference added, abstract and section 5 expanded, typos correcte

A note on a gauge-gravity relation and functional determinants

We present a refinement of a recently found gauge-gravity relation between one-loop effective actions: on the gauge side, for a massive charged scalar in 2d dimensions in a constant maximally symmetric electromagnetic field; on the gravity side, for a massive spinor in d-dimensional (Euclidean) anti-de Sitter space. The inclusion of the dimensionally regularized volume of AdS leads to complete mapping within dimensional regularization. In even-dimensional AdS, we get a small correction to the original proposal; whereas in odd-dimensional AdS, the mapping is totally new and subtle, with the `holographic trace anomaly' playing a crucial role.Comment: 6 pages, io

Quantum Field Dynamics in a Uniform Magnetic Field: Description using Fields in Oblique Phase Space

We present a simple field transformation which changes the field arguments from the ordinary position-space coordinates to the oblique phase-space coordinates that are linear in position and momentum variables. This is useful in studying quantum field dynamics in the presence of external uniform magnetic field: here, the field transformation serves to separate the dynamics within the given Landau level from that between different Landau levels. We apply this formalism to both nonrelativistic and relativistic field theories. In the large external magnetic field our formalism provides an efficient method for constructing the relevant lower-dimensional effective field theories with the field degrees defined only on the lowest Landau level.Comment: 27 pages, no figure

Mass Spectra of N=2 Supersymmetric SU(n) Chern-Simons-Higgs Theories

An algebraic method is used to work out the mass spectra and symmetry breaking patterns of general vacuum states in N=2 supersymmetric SU(n) Chern-Simons-Higgs systems with the matter fields being in the adjoint representation. The approach provides with us a natural basis for fields, which will be useful for further studies in the self-dual solutions and quantum corrections. As the vacuum states satisfy the SU(2) algebra, it is not surprising to find that their spectra are closely related to that of angular momentum addition in quantum mechanics. The analysis can be easily generalized to other classical Lie groups.Comment: 17 pages, use revte

Consistency restrictions on maximal electric field strength in QFT

QFT with an external background can be considered as a consistent model only if backreaction is relatively small with respect to the background. To find the corresponding consistency restrictions on an external electric field and its duration in QED and QCD, we analyze the mean energy density of quantized fields for an arbitrary constant electric field E, acting during a large but finite time T. Using the corresponding asymptotics with respect to the dimensionless parameter $eET^2$, one can see that the leading contributions to the energy are due to the creation of paticles by the electric field. Assuming that these contributions are small in comparison with the energy density of the electric background, we establish the above-mentioned restrictions, which determine, in fact, the time scales from above of depletion of an electric field due to the backreactionComment: 7 pages; version accepted for publication in Phys. Rev. Lett.; added one ref. and some comment