15,607 research outputs found

    Linear Form of Canonical Gravity

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    Recent work in the literature has shown that general relativity can be formulated in terms of a jet bundle which, in local coordinates, has five entries: local coordinates on Lorentzian space-time, tetrads, connection one-forms, multivelocities corresponding to the tetrads and multivelocities corresponding to the connection one-forms. The derivatives of the Lagrangian with respect to the latter class of multivelocities give rise to a set of multimomenta which naturally occur in the constraint equations. Interestingly, all the constraint equations of general relativity are linear in terms of this class of multimomenta. This construction has been then extended to complex general relativity, where Lorentzian space-time is replaced by a four-complex-dimensional complex-Riemannian manifold. One then finds a holomorphic theory where the familiar constraint equations are replaced by a set of equations linear in the holomorphic multimomenta, providing such multimomenta vanish on a family of two-complex-dimensional surfaces. In quantum gravity, the problem arises to quantize a real or a holomorphic theory on the extended space where the multimomenta can be defined.Comment: 5 pages, plain-te

    Superficial processing of explicit inferences in text

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    Research reported herein was supported in part by the National Institute of Education. US-NIE-C-400-76-0116Includes bibliographical references (leaf 20)Research reported herein was supported in part by the National Institute of Education. US-NIE-C-400-76-011

    Singularity Theory in Classical Cosmology

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    This paper compares recent approaches appearing in the literature on the singularity problem for space-times with nonvanishing torsion.Comment: 4 pages, plain-tex, published in Nuovo Cimento B, volume 107, pages 849-851, year 199

    Fast wavelength-tunable ultra-violet laser source for confocal Fura-2AM imaging

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    We report a novel wavelength-flexible laser source for three-dimensional ultra-violet imaging. Based on supercontinuum generation in photonic crystal fiber, the resultant broadband laser source extended from A = 331 nm into the visible region of the spectrum. Using an electronically-controlled filter wheel and filter set with a response time of approximately 50 ins, rapid wavelength selection was performed. The described scheme is capable of exciting the current range of ultra-violet-excited fluorophores and the simple and rapid wavelength control also provides a new approach for fast ratiometric imaging of Fura-2AM, facilitating an easy method of performing quantitative intracellular calcium concentration measurements

    Essential self-adjointness in one-loop quantum cosmology

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    The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper proves self-adjointness of these second-order elliptic operators.Comment: 14 pages, plain Tex. An Erratum has been added to the end, which corrects section

    Boundary Operators in Quantum Field Theory

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    The fundamental laws of physics can be derived from the requirement of invariance under suitable classes of transformations on the one hand, and from the need for a well-posed mathematical theory on the other hand. As a part of this programme, the present paper shows under which conditions the introduction of pseudo-differential boundary operators in one-loop Euclidean quantum gravity is compatible both with their invariance under infinitesimal diffeomorphisms and with the requirement of a strongly elliptic theory. Suitable assumptions on the kernel of the boundary operator make it therefore possible to overcome problems resulting from the choice of purely local boundary conditions.Comment: 23 pages, plain Tex. The revised version contains a new section, and the presentation has been improve

    Non-Locality and Ellipticity in a Gauge-Invariant Quantization

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    The quantum theory of a free particle in two dimensions with non-local boundary conditions on a circle is known to lead to surface and bulk states. Such a scheme is here generalized to the quantized Maxwell field, subject to mixed boundary conditions. If the Robin sector is modified by the addition of a pseudo-differential boundary operator, gauge-invariant boundary conditions are obtained at the price of dealing with gauge-field and ghost operators which become pseudo-differential. A good elliptic theory is then obtained if the kernel occurring in the boundary operator obeys certain summability conditions, and it leads to a peculiar form of the asymptotic expansion of the symbol. The cases of ghost operator of negative and positive order are studied within this framework.Comment: 17 pages, plain Te

    Binary Fluids with Long Range Segregating Interaction I: Derivation of Kinetic and Hydrodynamic Equations

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    We study the evolution of a two component fluid consisting of ``blue'' and ``red'' particles which interact via strong short range (hard core) and weak long range pair potentials. At low temperatures the equilibrium state of the system is one in which there are two coexisting phases. Under suitable choices of space-time scalings and system parameters we first obtain (formally) a mesoscopic kinetic Vlasov-Boltzmann equation for the one particle position and velocity distribution functions, appropriate for a description of the phase segregation kinetics in this system. Further scalings then yield Vlasov-Euler and incompressible Vlasov-Navier-Stokes equations. We also obtain, via the usual truncation of the Chapman-Enskog expansion, compressible Vlasov-Navier-Stokes equations.Comment: TeX, 50 page
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