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

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

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

Flavour-conserving oscillations of Dirac-Majorana neutrinos

We analyze both chirality-changing and chirality-preserving transitions of Dirac-Majorana neutrinos. In vacuum, the first ones are suppressed with respect to the others due to helicity conservation and the interactions with a (``normal'') medium practically does not affect the expressions of the probabilities for these transitions, even if the amplitudes of oscillations slightly change. For usual situations involving relativistic neutrinos we find no resonant enhancement for all flavour-conserving transitions. However, for very light neutrinos propagating in superdense media, the pattern of oscillations $\nu_L \to \nu^C_L$ is dramatically altered with respect to the vacuum case, the transition probability practically vanishing. An application of this result is envisaged.Comment: 14 pages, latex 2E, no figure

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

A new antisymmetric bilinear map for type-I gauge theories

In the case of gauge theories, which are ruled by an infinite-dimensional invariance group, various choices of antisymmetric bilinear maps on field functionals are indeed available. This paper proves first that, within this broad framework, the Peierls map (not yet the bracket) is a member of a larger family. At that stage, restriction to gauge-invariant functionals of the fields, with the associated Ward identities and geometric structure of the space of histories, make it possible to prove that the new map is indeed a Poisson bracket in the simple but relevant case of Maxwell theory. The building blocks are available for gauge theories only: vector fields that leave the action functional invariant; the invertible gauge-field operator, and the Green function of the ghost operator.Comment: 10 page

Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at one-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding one-loop divergences and one-loop effective action actually exists. The present paper shows that, on the Euclidean four-ball, only the scalar part of perturbative modes for quantum gravity are affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is confined to the remaining fourth sector. The integral representation of the resulting zeta-function asymptotics is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time.Comment: 25 pages, Revtex-4. Misprints in Eqs. (5.11), (5.14), (5.16) have been correcte

Focus on quantum thermodynamics

PublishedEditorialJournalThis is the final version of the article. Available from IOP Publishing via the DOI in this record.-This research was supported by the COST network MP1209 'Thermodynamics in the quantum regime'. JA acknowledges support by the Royal Society and UK's EPSRC (Project No. EP/M009165/1). ME acknowledges support by the National Research Fund Luxembourg (Project No. FNR/A11/02) and the European Research Council (Project No. 681456)

Can real-time visual feedback during gait retraining reduce metabolic demand for individuals with transtibial amputation?

The metabolic demand of walking generally increases following lower extremity amputation. This study used real-time visual feedback to modify biomechanical factors linked to an elevated metabolic demand of walking in individuals with transtibial amputation. Eight persons with unilateral, traumatic transtibial amputation and 8 uninjured controls participated. Two separate bouts of real-time visual feedback were provided during a single session of gait retraining to reduce 1) center of mass sway and 2) thigh muscle activation magnitudes and duration. Baseline and post-intervention data were collected. Metabolic rate, heart rate, frontal plane center of mass sway, quadriceps and hamstrings muscle activity, and co-contraction indices were evaluated during steady state walking at a standardized speed. Visual feedback successfully decreased center of mass sway 12% (p = 0.006) and quadriceps activity 12% (p = 0.041); however, thigh muscle co-contraction indices were unchanged. Neither condition significantly affected metabolic rate during walking and heart rate increased with center-of-mass feedback. Metabolic rate, center of mass sway, and integrated quadriceps muscle activity were all not significantly different from controls. Attempts to modify gait to decrease metabolic demand may actually adversely increase the physiological effort of walking in individuals with lower extremity amputation who are young, active and approximate metabolic rates of able-bodied adults