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

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

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

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

New Developments in the Spectral Asymptotics of Quantum Gravity

A vanishing one-loop wave function of the Universe in the limit of small three-geometry is found, on imposing diffeomorphism-invariant boundary conditions on the Euclidean 4-ball in the de Donder gauge. This result suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory. All of this is made possible by a peculiar spectral cancellation on the Euclidean 4-ball, here derived and discussed.Comment: 7 pages, latex file. Paper prepared for the Conference "QFEXT05: Quantum Field Theory Under the Influence of External Conditions", Barcelona, September 5 - September 9, 2005. In the final version, the presentation has been further improved, and yet other References have been adde

One-Loop Effective Action for Euclidean Maxwell Theory on Manifolds with Boundary

This paper studies the one-loop effective action for Euclidean Maxwell theory about flat four-space bounded by one three-sphere, or two concentric three-spheres. The analysis relies on Faddeev-Popov formalism and $\zeta$-function regularization, and the Lorentz gauge-averaging term is used with magnetic boundary conditions. The contributions of transverse, longitudinal and normal modes of the electromagnetic potential, jointly with ghost modes, are derived in detail. The most difficult part of the analysis consists in the eigenvalue condition given by the determinant of a $2 \times 2$ or $4 \times 4$ matrix for longitudinal and normal modes. It is shown that the former splits into a sum of Dirichlet and Robin contributions, plus a simpler term. This is the quantum cosmological case. In the latter case, however, when magnetic boundary conditions are imposed on two bounding three-spheres, the determinant is more involved. Nevertheless, it is evaluated explicitly as well. The whole analysis provides the building block for studying the one-loop effective action in covariant gauges, on manifolds with boundary. The final result differs from the value obtained when only transverse modes are quantized, or when noncovariant gauges are used.Comment: 25 pages, Revte