15,629 research outputs found
Linear Form of Canonical Gravity
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
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
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
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
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
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
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
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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