Conformal Anomaly for Free Scalar Propagation on Curved Bounded Manifolds

The trace anomaly for free propagation in the context of a conformally invariant scalar field theory defined on a curved manifold of positive constant curvature with boundary is evaluated through use of an asymptotic heat kernel expansion. In addition to their direct physical significance the results are also of relevance to the holographic principle and to Quantum Cosmology.Comment: 8 pages. To appear in General Relativity and Gravitatio

Gravitons in One-Loop Quantum Cosmology: Correspondence Between Covariant and Non-Covariant Formalisms

The discrepancy between the results of covariant and non-covariant one-loop calculations for higher-spin fields in quantum cosmology is analyzed. A detailed mode-by-mode study of perturbative quantum gravity about a flat Euclidean background bounded by two concentric 3-spheres, including non-physical degrees of freedom and ghost modes, leads to one-loop amplitudes in agreement with the covariant Schwinger-DeWitt method. This calculation provides the generalization of a previous analysis of fermionic fields and electromagnetic fields at one-loop about flat Euclidean backgrounds admitting a well-defined 3+1 decomposition.Comment: 29 pages, latex, recently appearing in Physical Review D, volume 50, pages 6329-6337, November 1994. The authors apologize for the delay in circulating the paper, due to technical problems now fixe

One-Loop Amplitudes in Euclidean Quantum Gravity

This paper studies the linearized gravitational field in the presence of boundaries. For this purpose, $\zeta$-function regularization is used to perform the mode-by-mode evaluation of BRST-invariant Faddeev-Popov amplitudes in the case of flat Euclidean four-space bounded by a three-sphere. On choosing the de Donder gauge-averaging term, the resulting $\zeta(0)$ value is found to agree with the space-time covariant calculation of the same amplitudes, which relies on the recently corrected geometric formulas for the asymptotic heat kernel in the case of mixed boundary conditions. Two sets of mixed boundary conditions for Euclidean quantum gravity are then compared in detail. The analysis proves that one cannot restrict the path-integral measure to transverse-traceless perturbations. By contrast, gauge-invariant amplitudes are only obtained on considering from the beginning all perturbative modes of the gravitational field, jointly with ghost modes.Comment: 26 pages, plain TeX, no figure

Analytical solution of a generalized Penna model

In 1995 T.J.Penna introduced a simple model of biological aging. A modified Penna model has been demonstrated to exhibit behaviour of real-life systems including catastrophic senescence in salmon and a mortality plateau at advanced ages. We present a general steady-state, analytic solution to the Penna model, able to deal with arbitrary birth and survivability functions. This solution is employed to solve standard variant Penna models studied by simulation. Different Verhulst factors regulating both the birth rate and external death rate are considered.Comment: 6 figure

Relativistic Gauge Conditions in Quantum Cosmology

This paper studies the quantization of the electromagnetic field on a flat Euclidean background with boundaries. One-loop scaling factors are evaluated for the one-boundary and two-boundary backgrounds. The mode-by-mode analysis of Faddeev-Popov quantum amplitudes is performed by using zeta-function regularization, and is compared with the space-time covariant evaluation of the same amplitudes. It is shown that a particular gauge condition exists for which the corresponding operator matrix acting on gauge modes is in diagonal form from the beginning. Moreover, various relativistic gauge conditions are studied in detail, to investigate the gauge invariance of the perturbative quantum theory.Comment: 26 pages, plain TeX, no figure

Come back Marshall, all is forgiven? : Complexity, evolution, mathematics and Marshallian exceptionalism

Marshall was the great synthesiser of neoclassical economics. Yet with his qualified assumption of self-interest, his emphasis on variation in economic evolution and his cautious attitude to the use of mathematics, Marshall differs fundamentally from other leading neoclassical contemporaries. Metaphors inspire more specific analogies and ontological assumptions, and Marshall used the guiding metaphor of Spencerian evolution. But unfortunately, the further development of a Marshallian evolutionary approach was undermined in part by theoretical problems within Spencer's theory. Yet some things can be salvaged from the Marshallian evolutionary vision. They may even be placed in a more viable Darwinian framework.Peer reviewedFinal Accepted Versio

Trends in heavy metals, polychlorinated biphenyls and toxicity from sediment cores of the inner River Thames estuary, London, UK

River islands (Ait or Eyot) within the inner tidal Thames serve as unique recorders of current and historical estuarine chemical pollution. Sediment cores from Chiswick Ait were assessed for contamination using Microtox® solid phase bioassay, stable isotopes (δ13C, δ15N), heavy metals and polychlorinated biphenyls (PCBs). Microtox® classified these sediments as non-toxic to moderately toxic and bulk isotopes identified a change in organic input. Metals Cu, Zn, Cr, Ni, Cd, Hg and Ag showed parallel rise, peak and fall profiles which when allied to a 207/208Pb and 137Cs based chronology supported major changes in trace metal contributions corresponding to approximate input times of 1940 (rise), 1963 (peak) and 1985 (fall). Metals ranged from Cu 15 to 373 mg kg−1 (mean 141 mg kg−1), Zn 137 to 1331 mg kg−1 (mean 576 mg kg−1), Cr 14–351 mg kg−1 (mean 156 mg kg−1), Pb 10 to 1506 mg kg−1 (mean 402 mg kg−1), As 1 to 107 (mean 38 mg kg−1), Ni 11 to 113 mg kg−1 (mean 63 mg kg−1), Cd 0.2 to 53 mg kg−1 (mean 9 mg kg−1), Hg 1 to 8 mg kg−1 (mean 4.6 mg kg−1) and Ag from 0.7 to 50 mg kg−1 (mean 7.5 mg kg−1). Down core total PCBs ranged from 10.5 to 121 μg kg−1 and mean of 39 μg kg−1. The rise, peak and fall of Cu, Zn, Cr, Ni, Cd and Ag pollution matched local sewage works' treatment discharge records. Whereas the Hg, Pb and As profiles were disconnected, reflecting alternative historic sources and or partitioning behaviour. Comparison to marine sediment quality guidelines indicate that Zn, Pb, Ni, Cd and Hg exceed action level 2, whereas sedimentary Cu, Cr and As concentrations were above action level 1 (no action) but below action level 2 (further investigation required). The river islands of the tidal Thames capture a unique contaminant chemistry record due in part to their location in the tidal frame (salinity minimum) and close proximity to west London

Resonant structure of space-time of early universe

A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes of wave function, penetrability $T_{\rm bar}$ and reflection $R_{\rm bar}$ relatively the barrier (accuracy of the method: $|T_{\rm bar}+R_{\rm bar}-1| < 1 \cdot 10^{-15}$), coefficient of penetration (i.e. probability of the packet to penetrate from the internal well outside with its tunneling), coefficient of oscillations (describing oscillating behavior of the packet inside the internal well). Using the method, evolution of universe in the closed Friedmann--Robertson--Walker model with quantization in presence of positive cosmological constant, radiation and component of generalize Chaplygin gas is studied. It is established (for the first time): (1) oscillating dependence of the penetrability on localization of start of the packet; (2) presence of resonant values of energy of radiation $E_{\rm rad}$, at which the coefficient of penetration increases strongly. From analysis of these results it follows: (1) necessity to introduce initial condition into both non-stationary, and stationary quantum models; (2) presence of some definite values for the scale factor $a$, where start of expansion of universe is the most probable; (3) during expansion of universe in the initial stage its radius is changed not continuously, but passes consequently through definite discrete values and tends to continuous spectrum in latter time.Comment: 18 pages, 14 figures, 4 table

Chiral bag boundary conditions on the ball

Local boundary conditions for spinor fields are expressed in terms of a 1-parameter family of boundary operators, and find applications ranging from (supersymmetric) quantum cosmology to the bag model in quantum chromodynamics. The present paper proves that, for massless spinor fields on the Euclidean ball in dimensions d=2,4,6, the resulting zeta(0) value is independent of such a theta parameter, while the various heat-kernel coefficients exhibit a theta-dependence which is eventually expressed in a simple way through hyperbolic functions and their integer powers.Comment: 30 pages, REVTe