Quantum Effective Action in Spacetimes with Branes and Boundaries

We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree level approximation. In the one-loop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions in the bulk factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the brane -- the inverse of the brane-to-brane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent well-known difficulties in heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowest order surface terms in the case of Robin and oblique boundary conditions. We briefly discuss multi-loop applications of the suggested Dirichlet reduction and the prospects of constructing the universal background field method for systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.Comment: LaTeX, 25 pages, final version, to appear in Phys. Rev.

Synchrotron X-ray microscopy of marine calcifiers: How plankton record past climate change

© Published under licence by IOP Publishing Ltd. We have used STXM and PEEM to reveal the underpinning chemistry and nanoscale structure behind palaeo-climate geochemical signatures, such as trace Mg in shells- proposed proxies for palaeo-ocean temperature. This has allowed us to test the chemical assumptions and mechanisms underpinning the use of such empirical proxies. We have determined the control on driving chemical variations in biogenic carbonates using STXM at the absorption edge of Mg, B, and Na in the shells of modern plankton. The power of these observations lies in their ability to link changes in chemistry, microstructure, and growth process in biogenic carbonate to environmental influences. We have seen that such changes occur at length scales of tens of nanometres and demonstrated that STXM provides an invaluable route to understanding chemical environment and key heterogeneity at the appropriate length scale. This new understanding provides new routes for future measurements of past climate variation in the sea floor fossil record

Synchrotron X-ray microscopy of marine calcifiers: how plankton record past climate change

We have used STXM and PEEM to reveal the underpinning chemistry and nanoscale structure behind palaeo-climate geochemical signatures, such as trace Mg in shells- proposed proxies for palaeo-ocean temperature. This has allowed us to test the chemical assumptions and mechanisms underpinning the use of such empirical proxies. We have determined the control on driving chemical variations in biogenic carbonates using STXM at the absorption edge of Mg, B, and Na in the shells of modern plankton. The power of these observations lies in their ability to link changes in chemistry, microstructure, and growth process in biogenic carbonate to environmental influences. We have seen that such changes occur at length scales of tens of nanometres and demonstrated that STXM provides an invaluable route to understanding chemical environment and key heterogeneity at the appropriate length scale. This new understanding provides new routes for future measurements of past climate variation in the sea floor fossil record

Effective action and heat kernel in a toy model of brane-induced gravity

We apply a recently suggested technique of the Neumann-Dirichlet reduction to a toy model of brane-induced gravity for the calculation of its quantum one-loop effective action. This model is represented by a massive scalar field in the $(d+1)$-dimensional flat bulk supplied with the $d$-dimensional kinetic term localized on a flat brane and mimicking the brane Einstein term of the Dvali-Gabadadze-Porrati (DGP) model. We obtain the inverse mass expansion of the effective action and its ultraviolet divergences which turn out to be non-vanishing for both even and odd spacetime dimensionality $d$. For the massless case, which corresponds to a limit of the toy DGP model, we obtain the Coleman-Weinberg type effective potential of the system. We also obtain the proper time expansion of the heat kernel in this model associated with the generalized Neumann boundary conditions containing second order tangential derivatives. We show that in addition to the usual integer and half-integer powers of the proper time this expansion exhibits, depending on the dimension $d$, either logarithmic terms or powers multiple of one quarter. This property is considered in the context of strong ellipticity of the boundary value problem, which can be violated when the Euclidean action of the theory is not positive definite.Comment: LaTeX, 20 pages, new references added, typos correcte

Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region

We suggest a method of construction of general diffeomorphism invariant boundary conditions for metric fluctuations. The case of $d+1$ dimensional Euclidean disk is studied in detail. The eigenvalue problem for the Laplace operator on metric perturbations is reduced to that on $d$-dimensional vector, tensor and scalar fields. Explicit form of the eigenfunctions of the Laplace operator is derived. We also study restrictions on boundary conditions which are imposed by hermiticity of the Laplace operator.Comment: LATeX file, no figures, no special macro

Further functional determinants

Functional determinants for the scalar Laplacian on spherical caps and slices, flat balls, shells and generalised cylinders are evaluated in two, three and four dimensions using conformal techniques. Both Dirichlet and Robin boundary conditions are allowed for. Some effects of non-smooth boundaries are discussed; in particular the 3-hemiball and the 3-hemishell are considered. The edge and vertex contributions to the $C_{3/2}$ coefficient are examined.Comment: 25 p,JyTex,5 figs. on request

Circumpolar Active-Layer Permafrost System (CAPS): a global geocryological database on CD and Internet (poster)

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The coordination and distribution of B in foraminiferal calcite

The isotopic ratio and concentration of B in foraminiferal calcite appear to reflect the pH and bicarbonate concentration of seawater. The use of B as a chemical proxy tracer has the potential to transform our understanding of the global carbon cycle, and ocean acidification processes. However, discrepancies between the theory underpinning the B proxies, and mineralogical observations of B coordination in biomineral carbonates call the basis of these proxies into question. Here, we use synchrotron X-ray spectromicroscopy to show that B is hosted solely as trigonal BO3 in the calcite test of Amphistegina lessonii, and that B concentration exhibits banding at the micron length scale. In contrast to previous results, our observation of trigonal B agrees with the predictions of the theoretical mechanism behind B palaeoproxies. These data strengthen the use of B for producing palaeo-pH records. The observation of systematic B heterogeneity, however, highlights the complexity of foraminiferal biomineralisation, implying that B incorporation is modulated by biological or crystal growth processes.We would like to acknowledge David Nicol, Iris Buisman and Martin Walker for invaluable technical assistance, and James Bryson for his help with synchrotron data collection. Wewould like to thank Jean DeMouthe (California Academy of Sciences) and Mike Rumsey (Natural History Museum, London) for provision of B-containing minerals for use as reference materials. This work was funded by ERC (grant 2010-ADG-267931 to HE), NERC, Jesus College (Cambridge)and the US Department of Energy (via ALS).This is the final published version. It first appeared at http://www.sciencedirect.com/science/article/pii/S0012821X15000849

Gauge-Averaging Functionals for Euclidean Maxwell Theory in the Presence of Boundaries

This paper studies the one-loop expansion of the amplitudes of electromagnetism about flat Euclidean backgrounds bounded by a 3-sphere, recently considered in perturbative quantum cosmology, by using zeta-function regularization. For a specific choice of gauge-averaging functional, the contributions to the full zeta value owed to physical degrees of freedom, decoupled gauge mode, coupled gauge modes and Faddeev-Popov ghost field are derived in detail, and alternative choices for such a functional are also studied. This analysis enables one to get a better understanding of different quantization techniques for gauge fields and gravitation in the presence of boundaries.Comment: 41 pages, plain-tex, recently appearing in Classical and Quantum Gravity, volume 11, pages 905-926, April 1994. The author wants to apologize for the delay in circulating the file, due to technical problems now fixe

K\"ahlerian Twistor Spinors

On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the K\"ahler structure, called K\"ahlerian twistor (Penrose) operator. We study K\"ahlerian twistor spinors and give a complete description of compact K\"ahler manifolds of constant scalar curvature admitting such spinors. As in the Riemannian case, the existence of K\"ahlerian twistor spinors is related to the lower bound of the spectrum of the Dirac operator.Comment: shorter version; to appear in Math.