Search results for "Variant"

U(N) invariant dynamics for a simplified loop quantum gravity model

2011

The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the recently introduced U(N) framework in order to construct SU(2) invariant operators and define a global U(N) symmetry that will select the homogeneous/isotropic states. Finally, we propose a Hamiltonian operator invariant under area-preserving deformations of the boundary surface and we identify possible connections of this model with Loop Quantum Cosmology.

Getting covariantly smeared sources into better shape

2014

The use of covariantly smeared sources in hadronic correlators is a common method of improving the projection onto the ground state. Studying the dependence of the shape of such sources on the gauge field background, we find that localized fluxes of magnetic field can strongly distort the sources. This results in a reduction of the smearing radii that can be reached by iterative smearing prescriptions, in particular as the continuum limit is approached. As a remedy, we propose a novel covariant smearing procedure (“free-form smearing”) enabling the creation of arbitrarily shaped sources, including in particular Gaussians of arbitrary radius, as well as shapes with nodes, such as hydrogenic …

Beyond the Minimal Standard Model

2011

The GSW theory is a great step forward in our understanding of electroweak interactions because it allows the well-known extremely successful theory of quantized electrodynamics and the theory of the weak CC and NC interactions to be cast into one unified, renormalizable local gauge theory. Renormalizability, in particular, is a very desirable property of the theory because it makes covariant perturbation theory a reasonable and well-defined approximation method for calculating physical quantities beyond the lowest order diagrams. Nevertheless, this model, very likely, is not the corner stone of a final theory of weak and electromagnetic interactions. It contains very many parameters which …

Central region in relativistic heavy ion collisions; results from hydrodynamic calculations and cascade simulation

1988

Results of three dimensional hydrodynamic calculations with boost invariant longitudinal expansion are presented with special emphasis on the transverse momentum spectra of hadrons and production rates of dileptons. The effect and signatures of transverse collective motion are discussed in detail. The hydrodynamic results which are based on the assumption of the existence of a first order phase transition and formation of an equilibrium mixed phase are compared with cascade simulation where the mixed phase is modelled in terms of plasma droplets embedded in a pion gas. The comparison shows a great deal of similarity between the two approaches lending further support for the hydrodynamic app…

2014

We investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large ra…

Type I vacuum solutions with aligned Papapetrou fields: an intrinsic characterization

2003

We show that Petrov type I vacuum solutions admitting a Killing vector whose Papapetrou field is aligned with a principal bivector of the Weyl tensor are the Kasner and Taub metrics, their counterpart with timelike orbits and their associated windmill-like solutions, as well as the Petrov homogeneous vacuum solution. We recover all these metrics by using an integration method based on an invariant classification which allows us to characterize every solution. In this way we obtain an intrinsic and explicit algorithm to identify them.

Covariant determination of the Weyl tensor geometry

2001

We give a covariant and deductive algorithm to determine, for every Petrov type, the geometric elements associated with the Weyl tensor: principal and other characteristic 2-forms, Debever null directions and canonical frames. We show the usefulness of these results by applying them in giving the explicit characterization of two families of metrics: static type I spacetimes and type III metrics with a hypersurface-orthogonal Killing vector. PACS numbers: 0240M, 0420C

On the invariant symmetries of the D-metrics

2007

We analyze the symmetries and other invariant qualities of the $\mathcal{D}$-metrics (type D aligned Einstein Maxwell solutions with cosmological constant whose Debever null principal directions determine shear-free geodesic null congruences). We recover some properties and deduce new ones about their isometry group and about their quadratic first integrals of the geodesic equation, and we analyze when these invariant symmetries characterize the family of metrics. We show that the subfamily of the Kerr-NUT solutions are those admitting a Papapetrou field aligned with the Weyl tensor.

Gravito-magnetic vacuum spacetimes: kinematic restrictions

2003

We show that there are no vacuum solutions with a purely magnetic Weyl tensor with respect to an observer submitted to kinematic restrictions involving first order differential scalars. This result generalizes previous ones for the vorticity-free and shear-free cases. We use a covariant approach which makes evident that only the Bianchi identities are used and, consequently, the results are also valid for non vacuum solutions with vanishing Cotton tensor.

A duality-invariant Einstein-Planck relation and its consequences on micro-black holes.

2013

We discuss the consequences of a duality-invariant Einstein–Planck (DIEP) relation on the equation of state of micro black holes. The results are analogous to those obtained from the "world-crystal" model, but with some significative differences, as for instance a limiting vanishing value for temperature for very small black holes. The model leads to a total evaporation of micro black holes but with the final stage being very slow.