Sitter Group Research Articles

Massless Spin-2 Rank-3 Tensor Field in de Sitter Universe

From the conformal transformation, a massless spin-2 field must be presented by a rank-3 mixed symmetric tensor field. A massless spin-2 rank-3 mixed symmetric tensor field in de Sitter ambient space formalism is studied in this paper, which may be regarded as the linearized gravity or its dual. Recalling the field equation, the possible physical solutions of the field equation are calculated. The solutions can be written in terms of a rank-2 symmetric tensor field and a scalar field. We discuss that under what conditions this tensor field can be associated with the de Sitter and conformal groups unitary representations. Finally, for the physical solution, the quantum field operator and the two-point function are presented.

Addition of a hospital bedside sitter during intracranial stereotactic EEG monitoring improves safety and seizure responses in an adult epilepsy monitoring unit

Expert consensus statements recommend continuous observation for patients undergoing intracranial electroencephalography (EEG), but this practice is neither universal nor specific regarding the type of observation. We compared outcomes for patients who underwent intracranial stereotactic EEG (SEEG) before and after the adoption of continuous monitoring by a staff bedside sitter.We retrospectively studied 26 consecutive adult patients who underwent SEEG placement at our center over a three-year period. Thirteen patients were monitored with usual protocol (no-sitter group), and 13 patients had a full-time hospital-employed sitter at bedside (sitter group). We analyzed nursing responses for all electroclinical seizures and characterized seizure-related adverse events.More seizures went unrecognized without a sitter (33.3% versus 15.0% of all seizures; p = 0.03). Two unrecognized focal to bilateral tonic–clonic seizures occurred only in the no-sitter group. Nursing response was significantly faster in the sitter group in relation to both electrographic seizure onset (12.0 s, p = 0.04) and clinical seizure onset (13.5 s, p = 0.02). Two patients in the no-sitter group pulled their electrodes out periictally while none did so in the sitter group.The addition of a full-time staff bedside sitter improved nursing response times and lowered the rate of unrecognized seizures in patients with SEEG monitoring. Sitters also helped to eliminate inadvertent major electrode displacement.

Physics of deformed special relativity: relativity principle revisited

In many different ways, Deformed Special Relativity (DSR) has been argued to provide an effective limit of quantum gravity in almost-flat regime. Unfortunately, DSR is up to now plagued by many conceptual problems (in particular how it describes macroscopic objects) which forbids a definitive physical interpretation and clear predictions. Here we propose a consistent framework to interpret DSR. We extend the principle of relativity: the same way that Special Relativity showed us that the definition of a reference frame requires to specify its speed, we show that DSR implies that we must also take into account its mass. We further advocate a 5- dimensional point of view on DSR physics and the extension of the kinematical symmetry from the Poincar´e group to the Poincaré-de Sitter group (ISO(4; 1)). This leads us to introduce the concept of a pentamomentum and to take into account the renormalization of the DSR deformation parameter kappa. This allows the resolution of the "soccer ball problem" (definition of many-particle-states) and provides a physical interpretation of the non-commutativity and non-associativity of the addition the relativistic quadrimomentum.

Some Properties of Massless Particles in Arbitrary Dimensions

Various properties of two kinds of massless representations of the n-conformal (or (n+1)-De Sitter) group [Formula: see text] are investigated for n≥2. It is found that, for space-time dimensions n≥3, the situation is quite similar to the one of the n=4 case for Sn-massless representations of the n-De Sitter group [Formula: see text]. These representations are the restrictions of the singletons of [Formula: see text]. The main difference is that they are not contained in the tensor product of two UIRs with the same sign of energy when n>4, whereas it is the case for another kind of massless representations. Finally some examples of Gupta–Bleuler triplets are given for arbitrary spin and n≥3.

Geometrical interpretation of In�n�-Wigner contractions

The Inonu-Wigner contractions which interrelate the Lie algebras of the isometry groups of metric spaces are discussed with reference to deformations of the absolutes of the spaces. A general formula is derived for the Lie algebra commutation relations of the isometry group for anyN-dimensional metric space. These ideas are illustrated by a discussion of important particular cases, which interrelate the four-dimensional de Sitter, Poincare, and Galilean groups.

Graded de Sitter space-time, group and algebra

The (m+n)-dimensional flat superspace is considered and graded linear groups with their graded algebra are calculated. The (4+4)-dimensional graded de Sitter space-time is discussed geometrically by its embedding in the (5+4)-dimensional flat superspace, and its isometry subgroupOSp¼ is calculated. We have used the isomorphism between the algebra ofSp4,R andSO3,2 to express the generatorsSab ofSO3,2 in terms of the generatorshαβ of the symplectic groupSp4,R, then it is easy to obtain the graded de Sitter algebra from the orthosymplectic algebraOSp¼. Finally, by contraction we obtain the graded Poincare algebra, that is the superalgebra with which we are familiar.

Field Theory of Particles with Arbitrary Spin

It is pointed out that existing field equations for particles of higher spin are unsuitable' for the formulation of field theories with interaction. ' A generalization of the Dirac and Kemmer matrices is discussed in terms of finite-dimensional representations of the de, Sitter group. ' It is shown how to formulate a general field theory in such a way as to exhibit a corresponding dynamical symmetry. The resulting field equation resembles Bhabha's, but is self-consistent in its applications to interacting particles and has a different type of mass spectrum. In the Appendix, it is shown that'within any'irreducible representation of the Poincare group there are finite-dimensional representations of the'Lorentz group'labelled (s, � s).