Teleparallel spin connection

A new expression for the spin connection of teleparallel gravity is proposed, given by minus the contorsion tensor plus a zero connection. The corresponding minimal coupling is covariant under local Lorentz transformation, and equivalent to the minimal coupling prescription of general relativity. With this coupling prescription, therefore, teleparallel gravity turns out to be fully equivalent to general relativity, even in the presence of spinor fields.

Gravitation and the local symmetry group of space-time

According to general relativity, the interaction of a matter field with gravitation requires the simultaneous introduction of a tetrad field, which is a field related to translations, and a spin connection, which is a field assuming values in the Lie algebra of the Lorentz group. These two fields, however, are not independent. By analyzing the constraint between them, it is concluded that the relevant local symmetry group behind general relativity is provided by the Lorentz group. Furthermore, it is shown that the minimal coupling prescription obtained from the Lorentz covariant derivative coincides exactly with the usual coupling prescription of general relativity. Instead of the tetrad, therefore, the spin connection is to be considered as the fundamental field representing gravitation.

Chiral asymmetry and gravitation theory

In this letter we apply an alternative approach, recently developed, to the description of massless particles of arbitrary spin to the case of spin-two particles. This provides a non-geometrical approach to the theory of linearized gravitation. Within this method the chiral components of a spinor field are treated as independent field variables. The free field Lagrangian is built up from the requirement of chiral invariance. This formulation is parallel to the neutrino theory and leads to a formulation that generalizes, to particles of spin-two, the two-component neutrino theory. At the free field level the analog of curvature tensor, spin connection tensor, and metric tensor are independent quantities. By introducing left-right asymmetric linear interactions of these chiral components we get the linearized gravitation theory.

Cartan geometry of spacetimes with a nonconstant cosmological function Lambda

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Konstruktion und Analyse einer funktionalen Renormierungsgruppengleichung für Gravitation im Einstein-Cartan-Zugang

Während das Standardmodell der Elementarteilchenphysik eine konsistente, renormierbare Quantenfeldtheorie dreier der vier bekannten Wechselwirkungen darstellt, bleibt die Quantisierung der Gravitation ein bislang ungelöstes Problem. In den letzten Jahren haben sich jedoch Hinweise ergeben, nach denen metrische Gravitation asymptotisch sicher ist. Das bedeutet, daß sich auch für diese Wechselwirkung eine Quantenfeldtheorie konstruieren läßt. Diese ist dann in einem verallgemeinerten Sinne renormierbar, der nicht mehr explizit Bezug auf die Störungstheorie nimmt. Zudem sagt dieser Zugang, der auf der Wilsonschen Renormierungsgruppe beruht, die korrekte mikroskopische Wirkung der Theorie voraus. Klassisch ist metrische Gravitation auf dem Niveau der Vakuumfeldgleichungen äquivalent zur Einstein-Cartan-Theorie, die das Vielbein und den Spinzusammenhang als fundamentale Variablen verwendet. Diese Theorie besitzt allerdings mehr Freiheitsgrade, eine größere Eichgruppe, und die zugrundeliegende Wirkung ist von erster Ordnung. Alle diese Eigenschaften erschweren eine zur metrischen Gravitation analoge Behandlung.rnrnIm Rahmen dieser Arbeit wird eine dreidimensionale Trunkierung von der Art einer verallgemeinerten Hilbert-Palatini-Wirkung untersucht, die neben dem Laufen der Newton-Konstante und der kosmologischen Konstante auch die Renormierung des Immirzi-Parameters erfaßt. Trotz der angedeuteten Schwierigkeiten war es möglich, das Spektrum des freien Hilbert-Palatini-Propagators analytisch zu berechnen. Auf dessen Grundlage wird eine Flußgleichung vom Propertime-Typ konstruiert. Zudem werden geeignete Eichbedingungen gewählt und detailliert analysiert. Dabei macht die Struktur der Eichgruppe eine Kovariantisierung der Eichtransformationen erforderlich. Der resultierende Fluß wird für verschiedene Regularisierungsschemata und Eichparameter untersucht. Dies liefert auch im Einstein-Cartan-Zugang berzeugende Hinweise auf asymptotische Sicherheit und damit auf die mögliche Existenz einer mathematisch konsistenten und prädiktiven fundamentalen Quantentheorie der Gravitation. Insbesondere findet man ein Paar nicht-Gaußscher Fixpunkte, das Anti-Screening aufweist. An diesen sind die Newton-Konstante und die kosmologische Konstante jeweils relevante Kopplungen, wohingegen der Immirzi-Parameter an einem Fixpunkt irrelevant und an dem anderen relevant ist. Zudem ist die Beta-Funktion des Immirzi-Parameters von bemerkenswert einfacher Form. Die Resultate sind robust gegenüber Variationen des Regularisierungsschemas. Allerdings sollten zukünftige Untersuchungen die bestehenden Eichabhängigkeiten reduzieren.

Investigations on asymptotic safety of metric, tetrad and Einstein-Cartan gravity

Among the different approaches for a construction of a fundamental quantum theory of gravity the Asymptotic Safety scenario conjectures that quantum gravity can be defined within the framework of conventional quantum field theory, but only non-perturbatively. In this case its high energy behavior is controlled by a non-Gaussian fixed point of the renormalization group flow, such that its infinite cutoff limit can be taken in a well defined way. A theory of this kind is referred to as non-perturbatively renormalizable. In the last decade a considerable amount of evidence has been collected that in four dimensional metric gravity such a fixed point, suitable for the Asymptotic Safety construction, indeed exists. This thesis extends the Asymptotic Safety program of quantum gravity by three independent studies that differ in the fundamental field variables the investigated quantum theory is based on, but all exhibit a gauge group of equivalent semi-direct product structure. It allows for the first time for a direct comparison of three asymptotically safe theories of gravity constructed from different field variables. The first study investigates metric gravity coupled to SU(N) Yang-Mills theory. In particular the gravitational effects to the running of the gauge coupling are analyzed and its implications for QED and the Standard Model are discussed. The second analysis amounts to the first investigation on an asymptotically safe theory of gravity in a pure tetrad formulation. Its renormalization group flow is compared to the corresponding approximation of the metric theory and the influence of its enlarged gauge group on the UV behavior of the theory is analyzed. The third study explores Asymptotic Safety of gravity in the Einstein-Cartan setting. Here, besides the tetrad, the spin connection is considered a second fundamental field. The larger number of independent field components and the enlarged gauge group render any RG analysis of this system much more difficult than the analog metric analysis. In order to reduce the complexity of this task a novel functional renormalization group equation is proposed, that allows for an evaluation of the flow in a purely algebraic manner. As a first example of its suitability it is applied to a three dimensional truncation of the form of the Holst action, with the Newton constant, the cosmological constant and the Immirzi parameter as its running couplings. A detailed comparison of the resulting renormalization group flow to a previous study of the same system demonstrates the reliability of the new equation and suggests its use for future studies of extended truncations in this framework.

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

Percolation and cluster Monte Carlo dynamics for spin models

A general scheme for devising efficient cluster dynamics proposed in a previous paper [Phys. Rev. Lett. 72, 1541 (1994)] is extensively discussed. In particular, the strong connection among equilibrium properties of clusters and dynamic properties as the correlation time for magnetization is emphasized. The general scheme is applied to a number of frustrated spin models and the results discussed.

Spin-1 duality in D dimensions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Time evolution of the Wigner function in discrete quantum phase space for a soluble quasi-spin model

The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wi:ner function is written for some chosen states associated to discrete angle and angular momentum variables, and the rime evolution is numerically calculated using the discrete von Neumnnn-Liouville equation. Direct evidences in the lime evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU(2)-based semiclassical continuous approach to the Lipkin model is also presented.

Higher spin symmetries and w∞ algebra in the conformal affine Toda model

As recently shown the conformal affine Toda models can be obtained via hamiltonian reduction from a two-loop Kac-Moody algebra. In this paper we propose a systematic procedure to analyze the higher spin symmetries of the conformal affine Toda models. The method is based on an explicit construction of infinite towers of extended conformal symmetry generators. Two fundamental building blocks of this construction are special spin-one and -two primary fields characterizing the conformal structure of these models. The connection to the algebra of area preserving diffeomorphisms on a two-manifold (w∞ algebra) is established.

Spin squeezing and entanglement via finite-dimensional discrete phase-space description

We show how mapping techniques inherent to N2-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the time evolution of certain special parameters related to the Robertson- Schrödinger (RS) uncertainty principle and some particular proposals of entanglement measure based on collective angular-momentum generators. Our results reinforce the connection between both the squeezing and entanglement effects, as well as allow to investigate the basic role of spin correlations through the discrete representatives of quasiprobability distribution functions. Entropy functionals are also discussed in this context. The main sequence correlations → entanglement → squeezing of quantum effects embraces a new set of insights and interpretations in this framework, which represents an effective gain for future researches in different spin systems. © 2013 World Scientific Publishing Company.

Modellkomplexe oligonuklearer Metalloproteine auf Basis von Salen-Liganden und Spin-Crossover-Verbindungen als Chemosensoren

Der erste Teil der hier vorgestellten Arbeit verfolgt die Synthese potentieller Modellverbindungen oligonuklearer Metalloproteine auf Basis von Salen-Liganden. Dazu wurden zwei Ligandensysteme mit unterschiedlich raumerfüllenden Alkyl-Substituenten modifiziert und auf ihre koordinativen Eigenschaften hin untersucht. Für das Ligandensystem auf Basis des Bis-(salicylidenamino)-propan-2-ols konnten fünf Derivate (H3L1, H3L2A,H3L2B, H3L3, H3L4), für das zweite verwendete Ligandensystem auf Basis des 1H-3,5-Bis-(salicylidenaminomethyl)-pyrazols konnten zwei weitere Derivate (H3L5A, H3L5B) dargestellt und zu Koordinationsverbindungen umgesetzt werden.rnFür den hier verwendeten Bis-(salicylidenamino)-propan-2-ol Liganden H3L1, welcher die geringsten sterischen Anforderungen stellt, konnten mono-, tri- und tetranukleare Koordinationsverbindungen synthetisiert werden. Dabei gelingt es dem Liganden, sich sowohl in planarer als auch in unterschiedlich stark gewinkelter Konformation um ein oder mehrere Metallzentren anzuordnen, wobei der Ligand ein N2O2- seines N2O3-Donorsets zur Koordination nutzt. Die Verbindung {[Ni7(HL1)2(L1)2(OBz)4(OMe)(H2O)]}n zeigt, dass eine Verkettung der so gestalteten dreikernigen Einheiten über das freie Propanol-Sauerstoffatomdes Ligandenrückgrats möglich ist. Mit zunehmendem sterischen Anspruch der angefügten Alkylsubstituenten nimmt die geometrische Flexibilität und somit das Potential des Liganden zur Ausbildung höhernuklearer Strukturen ab. So ist für Liganden mit mittlerem sterischen Anspruch neben mononuklearen Komplexen noch die Gestaltung dinuklearer Systeme möglich. Erhöht man den sterischen Anspruch des Liganden weiter, findet nur noch eine Reaktion zu mononuklearen Verbindungen statt.rnMit den Pyrazol-basierten Ligandensystemen H3L5A und H3L5B konnten dinukleare Kupfer- und Nickelverbindungen synthetisiert werden.rnDer zweite Teil dieser Arbeit befasst sich mit der Gestaltung von Spin-Crossover Systemen (SCO). Dazu soll ein Spinübergang innerhalb des gestalteten schaltbaren Systems an die Anwesenheit eines Signalstoffs gekoppelt werden, so dass diese SCO-Verbindung als Sensor für den Signalstoff eingesetzt werden kann. Dazu wurden zwei unterschiedliche Ansätze entwickelt und untersucht.rnDie erste Methode beruht auf der Kombination eines zum Spin-Crossover befähigten Metallzentrums, eines Capping-Liganden, eines zur Signalstofferkennung funktionalisierten Co-Liganden sowie eines entsprechenden Signalstoffs. Als Capping-Liganden wurden tetra- und pentadentateLigandensysteme eingesetzt und mit unterschiedlich Picolyl-substituierten Monoaza-[12]-krone-4-Derivaten umgesetzt, wobei die Monoazakrone zur Komplexierung des Signalstoffs,hier in Form eines Alkalimetallions, zur Verfügung steht. Nach dieser ersten Methode konnten im Zeitraum dieser Arbeit noch keine zufriedenstellenden Ergebnisse erzielt werden.rnEine vielversprechende zweite Möglichkeit beruht auf der Verwendung eines mehrzähnigen, etablierten Spin-Crossover Liganden,welcher in seiner Peripherie mit einer Bindungstasche zur Aufnahme des Signalstoffmodifiziert wird.Mit Hilfe des so gestalteten Liganden 4'-(4'''-Benzo-[15]-krone-5)-methyloxy-2,2':6',2''-terpyridin ([b15c5]-tpy) gelang die Umsetzung zu entsprechenden Eisen(II)- und Kobalt(II)komplexen der Zusammensetzung [M([b15c5]-tpy)2]2+. Alle synthetisierten Eisen(II)-Komplexe liegen aufgrund der hohen Ligandenfeldstärke des Terpyridins über einen Temperaturbereich von 300 – 400 K in ihrer diamagnetischen Low Spin Form vor. Die entsprechenden Kobalt(II)-Komplexe zeigen über einen Temperaturbereich von 2 – 350 K ein kontinuierliches, aber unvollständiges Spin-Crossover Verhalten.rnDer Einfluss von Signalstoffen auf das Spin-Crossover Verhalten der Kobalt(II)-Systeme wurde in einem ersten Versuch unter der Verwendung von Natriumionen als Signalstoff untersucht. Dabei stellte sich heraus, dass Natriumionen für dieses System zwar nicht als Auslöser eines SCO verwendet werden können, sie aber dennoch eine starke Auswirkung auf den Verlauf des Spin-Crossovers haben.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.

Extreme Harmonic Generation In Electrically Driven Spin Resonance.

We report the observation of multiple harmonic generation in electric dipole spin resonance in an InAs nanowire double quantum dot. The harmonics display a remarkable detuning dependence: near the interdot charge transition as many as eight harmonics are observed, while at large detunings we only observe the fundamental spin resonance condition. The detuning dependence indicates that the observed harmonics may be due to Landau-Zener transition dynamics at anticrossings in the energy level spectrum.