Extrinsic Killing spinors

 Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of non-negative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary isometric to a round sphere, is necessarily a flat disc. Received: 2 February 2002; in final form: 1 August 2002 / Published online: 1 April 2003 Mathematics Subject Classification (1991): 53C27, 53C40, 53C80, 58G25 The authors would like to thank Lars Andersson for helpful discussions and for bringing to our knowledge the information regarding Remark 4. We are also grateful to the referee for pointing out that Corollary 5 and Corollary 6 are only valid when the boundary is at least 2-dimensional. Research of S. Montiel is partially supported by a Spanish MCyT grant No. BFM2001-2967     

Gauge anomaly cancellation in chiral gauge theories

We consider chiral fermions interacting minimally with abelian and non-abelian gauge fields. Using a path integral approach and exploring the consequences of a mechanism of symmetry restoration, we show that the gauge anomaly has null expectation value in the vacuum for both cases (abelian and non-abelian). We argue that the same mechanism has no possibility to cancel the chiral anomaly, what eliminates competition between chiral and gauge symmetry at full quantum level. We also show that the insertion of the gauge anomaly in arbitrary gauge invariant correlators gives a null result, which points towards anomaly cancellation in the subspace of physical state vectors.     

Eigenvalues of the Dirac Operator on Manifolds¶with Boundary

Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. For the local boundary conditions, limiting cases are characterized by the existence of real Killing spinors and the minimality of the boundary. Received: 22 August 2000 / Accepted: 15 March 2001     

Modal-Hamiltonian Interpretation of Quantum Mechanics and Casimir Operators: The Road Toward Quantum Field Theory

The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) fields. In this case we propose that the actual-valued observables are the Casimir operators of the Poincaré group and of the group U(1) of the internal symmetry of the theory. Moreover, we also show that the magnitudes that acquire actual values in the relativistic and in the non-relativistic cases are correctly related through the adequate limit.     

Implications of obesity for tendon structure, ultrastructure and biochemistry: a study on Zucker rats

The extracellular matrix consists of collagen, proteoglycans and non-collagen proteins. The incidence of obesity and associated diseases is currently increasing in developed countries. Obesity is considered to be a disease of modern times, and genes predisposing to the disease have been identified in humans and animals. The objective of the present study was to compare the morphological and biochemical aspects of the deep digital flexor tendon of lean (Fa/Fa or Fa/fa) and genetically obese (fa/fa) Zucker rats. Ultrastructural analysis showed the presence of lipid droplets in both groups, whereas disorganized collagen fibril bundles were observed in obese animals. Lean animals presented a larger amount of non-collagen proteins and glycosaminoglycans than obese rats. We propose that the overweight and lesser physical activity in obese animals may have provoked the alterations in the composition and organization of extracellular matrix components but a genetic mechanism cannot be excluded. These alterations might be related to organizational and structural modifications in the collagen bundles that influence the mechanical properties of tendons and the progression to a pathological state.     

Current-induced exchange interactions and effective temperature in localized moment systems

We study theoretically the spin dynamics of a magnetic dimer serving as a contact between two electrodes. We find that the spin-spin coupling in the dimer can be dramatically modified from its equilibrium value. We show that the interaction can be tuned in such a way that it effectively changes its sign. The calculations show that, for large enough bias, the exchange interaction can even be changed from antiferromagnetic to ferromagnetic. The physical principles behind this result can be used as a new tool to achieve magneto-electric effects in molecular magnet systems.     

Novel pulsed switched power supply for a fast field cycling NMR spectrometer

In this paper, we outline the operating principles of a pulsed switched power supply for a fast field-cycling nuclear magnetic resonance spectrometer. The power supply uses a variant of a four-quadrant chopper with a duty cycle that defines the average output current. With this topology only two semiconductors are necessary to drive hundreds of amperes with an output power of several kilowatts. The output current ripple has a well-defined shape that can be reduced to acceptable values by a careful design of the semiconductors' controlling circuits and drivers. A power supply prototype was tested with a home build air-core magnet operating with fields between 0 and 0.21 T. The system is computer controlled using pulse generator and data acquisition PC cards, and specific user-friendly home-developed software. A comparative proton relaxometry study in two well-known liquid crystal compounds 5CB and MBBA was performed to check the reproducibility of the T1 measurements.     

Tuning the Lewis acid phenol $$\varvec{}$$-prenylation as a molecular diversity tool

A diversity-oriented approach for the synthesis of various structurally different prenylated alcohols from readily accessible and common precursors was developed. With varying approaches, this article describes some successful examples of a Friedel–Crafts alkylation using methoxyphenols and different prenyl alcohols (geraniol and (E,E)-farnesol). We demonstrated that just by varying the stoichiometry of the Lewis acid used, the course of the reaction can be shifted to produce the alkylated or the cyclized product. Eighteen unique products were obtained with good isolated yields by direct alkylation with or without a consecutive \(\pi \)-cationic cyclization.