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49
Metricaffine f(R) theories of gravity
 J. Suppl. Ser
, 2007
"... Modified gravity theories have received increased attention lately due to combined motivation coming from highenergy physics, cosmology and astrophysics. Among numerous alternatives to Einstein’s theory of gravity, theories which include higher order curvature invariants, and specifically the parti ..."
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Modified gravity theories have received increased attention lately due to combined motivation coming from highenergy physics, cosmology and astrophysics. Among numerous alternatives to Einstein’s theory of gravity, theories which include higher order curvature invariants, and specifically the particular class of f(R) theories, have a long history. In the last five years there has
Error propagation framework for diffusion tensor imaging
 Proc. Int. Soc. Magn. Reson. Med
, 2006
"... Abstract—An analytical framework of error propagation for diffusion tensor imaging (DTI) is presented. Using this framework, any uncertainty of interest related to the diffusion tensor elements or to the tensorderived quantities such as eigenvalues, eigenvectors, trace, fractional anisotropy (FA), ..."
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Abstract—An analytical framework of error propagation for diffusion tensor imaging (DTI) is presented. Using this framework, any uncertainty of interest related to the diffusion tensor elements or to the tensorderived quantities such as eigenvalues, eigenvectors, trace, fractional anisotropy (FA), and relative anisotropy (RA) can be analytically expressed and derived from the noisy diffusionweighted signals. The proposed framework elucidates the underlying geometric relationship between the variability of a tensorderived quantity and the variability of the diffusion weighted signals through the nonlinear least squares objective function of DTI. Monte Carlo simulations are carried out to validate and investigate the basic statistical properties of the proposed framework. Index Terms—Cone of uncertainty, covariance structures, diffusion tensor imaging, diffusion tensor representations, error propagation, invariant Hessian. I.
Actions for gravity with generalizations: a review
, 1994
"... The search for a theory of quantum gravity has for a long time been almost fruitless. A few years ago, however, Ashtekar found a reformulation of Hamiltonian gravity, which thereafter has given rise to a new promising quantization project; the canonical Dirac quantization of Einstein gravity in term ..."
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The search for a theory of quantum gravity has for a long time been almost fruitless. A few years ago, however, Ashtekar found a reformulation of Hamiltonian gravity, which thereafter has given rise to a new promising quantization project; the canonical Dirac quantization of Einstein gravity in terms of Ahtekar’s new variables. This project has already given interesting results, although many important ingredients are still missing before we can say that the quantization has been successful. Related to the classical Ashtekar Hamiltonian, there have been discoveries regarding new classical actions for gravity in (2+1) and (3+1)dimensions, and also generalizations of Einstein’s theory of gravity. In the first type of generalization, one introduces infinitely many new parameters, similar to the conventional Einstein cosmological constant, into the theory. These generalizations are called ”neighbours of Einstein’s theory ” or ”cosmological constants generalizations”, and the theory has the same number of degrees of freedom, per point in spacetime, as the conventional Einstein theory. The second type is a gauge group generalization of Ashtekar’s Hamiltonian, and this theory has the correct number
SL(2, C) gravity with complex vierbein and its noncommutative extension,” Phys
 Rev. D
"... We show that it is possible to formulate gravity with a complex vierbein based on SL(2, C) gauge invariance. The proposed action is a fourform where the metric is not introduced but results as a function of the complex vierbein. This formulation is based on the first order formalism. The novel feat ..."
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We show that it is possible to formulate gravity with a complex vierbein based on SL(2, C) gauge invariance. The proposed action is a fourform where the metric is not introduced but results as a function of the complex vierbein. This formulation is based on the first order formalism. The novel feature here is that integration of the spinconnection gauge field gives rise to kinetic terms for a massless graviton, a massive graviton with the FierzPauli mass term, and a scalar field. The resulting theory is equivalent to bigravity. We then show that by extending the gauge group to GL(2, C) the formalism can be easily generalized to apply to a noncommutative space with the star product. We give the deformed action to second order in the deformation parameter, and derive the SeibergWitten map for the complex vierbein and gauge fields.
Classical electrodynamics: A Tutorial on its Foundations. In Quo vadis geodesia...? Festschrift for
 Eprint Archive
, 1999
"... We will display the fundamental structure of classical electrodynamics. Starting from the axioms of (1) electric charge conservation, (2) the existence of a Lorentz force density, and (3) magnetic flux conservation, we will derive Maxwell’s equations. They are expressed in terms of the field strengt ..."
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We will display the fundamental structure of classical electrodynamics. Starting from the axioms of (1) electric charge conservation, (2) the existence of a Lorentz force density, and (3) magnetic flux conservation, we will derive Maxwell’s equations. They are expressed in terms of the field strengths (E, B), the excitations (D,H), and the sources (ρ,j). This fundamental set of four microphysical equations has to be supplemented by somewhat less general constitutive assumptions in order to make it a fully determined system with a wellposed initial value problem. It is only at this stage that a distance concept (metric) is required for spacetime. We will discuss one set of possible constitutive assumptions, namely D ∼ E and H ∼ B. file erik8a.tex,
Torsion waves in metric–affine field theory
, 2000
"... Abstract. The approach of metric–affine field theory is to define spacetime as a real oriented 4manifold equipped with a metric and an affine connection. The 10 independent components of the metric tensor and the 64 connection coefficients are the unknowns of the theory. We write the Yang–Mills act ..."
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Abstract. The approach of metric–affine field theory is to define spacetime as a real oriented 4manifold equipped with a metric and an affine connection. The 10 independent components of the metric tensor and the 64 connection coefficients are the unknowns of the theory. We write the Yang–Mills action for the affine connection and vary it both with respect to the metric and the connection. We find a family of spacetimes which are stationary points. These spacetimes are waves of torsion in Minkowski space. We then find a special subfamily of spacetimes with zero Ricci curvature; the latter condition is the Einstein equation describing the absence of sources of gravitation. A detailed examination of this special subfamily suggests the possibility of using it to model the neutrino. Our model naturally contains only two distinct types of particles which may be identified with lefthanded neutrinos and righthanded antineutrinos.
On the Equivalence Principle and a Unified Description of Gravitation and Electromagnetism
"... We first investigate the form the general relativity theory would have taken had the gravitational mass and the inertial mass of material objects been different. We then extend this analysis to electromagnetism and postulate an equivalence principle for the electromagnetic field. We argue that to ea ..."
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We first investigate the form the general relativity theory would have taken had the gravitational mass and the inertial mass of material objects been different. We then extend this analysis to electromagnetism and postulate an equivalence principle for the electromagnetic field. We argue that to each particle with a different electric chargetomass ratio in a gravitational and electromagnetic field there corresponds a spacetime manifold whose metric tensor gµν describes the dynamical actions of gravitation and electromagnetism. The possibility of exhibiting gravitation and electromagnetism in a unified geometrical representation has been pursued by many mathematicians and physicists. The first one to seek for a unified explanation of gravitation and electromagnetism was Riemann (see ref.[1]). This endeavor has really started as a fullfledged research area soon after the advent of Einstein’s general theory in 1916 [2]. The gaugeinvariant unified theory of Weyl was based on a generalization of Riemannian geometry [3,4]. A generalization of Weyl’s theory was put forward by Eddington
Dualitysymmetric gravity and supergravity: testing the PST approach
 Ukr. J. Phys
"... Abstract. Drawing an analogy between gravity dynamical equation of motion and that of Maxwell electrodynamics with an electric source we outline a way of appearance of a dual to graviton field. We propose a dimensional reduction ansatz for the field strength of this field which reproduces the correc ..."
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Abstract. Drawing an analogy between gravity dynamical equation of motion and that of Maxwell electrodynamics with an electric source we outline a way of appearance of a dual to graviton field. We propose a dimensional reduction ansatz for the field strength of this field which reproduces the correct duality relations between fields arising in the dimensional reduction of Ddimensional gravity action to D1 dimensions. Modifying the PST approach we construct a new term entering the action of D=11 dualitysymmetric gravity and by use of the proposed ansatz we confirm the relevance of such a term to reproduce the correct dualitysymmetric structure of the reduced theory. We end up extending the results to the bosonic sector of D=11 supergravity. Contents
Early Greek Thought and perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach
 In The Blue Book of Einstein Meets Magritte
, 1999
"... It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a reevaluation of the main paradox of early Greek thought: the paradox of Being and nonBeing, and the solutions presented to it by Plato and Ari ..."
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It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a reevaluation of the main paradox of early Greek thought: the paradox of Being and nonBeing, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the coincidence of being and nonbeing in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato’s Theory of Forms and Aristotle’s metaphysics and logic. Plato’s and Aristotle’s systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object,
Novel Geometric Gauge Invariance of Autoparallels. Eprint
, 1998
"... We draw attention to a novel type of geometric gauge invariance relating the autoparallel equations of motion in different RiemannCartan spacetimes with each other. The novelty lies in the fact that the equations of motion are invariant even though the actions are not. As an application we use this ..."
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We draw attention to a novel type of geometric gauge invariance relating the autoparallel equations of motion in different RiemannCartan spacetimes with each other. The novelty lies in the fact that the equations of motion are invariant even though the actions are not. As an application we use this gauge transformation to map the action of a spinless point particle in a RiemannCartan spacetime with a gradient torsion to a purely Riemann spacetime, in which the initial torsion appears as a nongeometric external field. By extremizing the transformed action in the usual way, we obtain the same autoparallel equations of motion as those derived in the initial spacetime with torsion via a recentlydiscovered variational principle. 1.