Results 1 - 10 of 1134
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[en] Consider a Riemannian manifold in dimension with a strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem is closely related to elastic qP-wave tomography. Under the condition that the manifold can be foliated with a continuous family of strictly convex hypersurfaces, the local invertibility implies a global result. One can straightforwardedly adapt the proof to show similar results for tensor fields of arbitrary rank. (paper)
[en] A general scalar–tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan frames using quantities that are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field. By comparing spectral indices, calculated up to second order, we find that the frames are equivalent up to this order, due to the underlying assumptions. (paper)
[en] Relevant algebraic structures for the description of quantum mechanics in the Heisenberg picture are replaced by tensor fields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group. (paper)
[en] The problem of connections between submanifolds with semiparallel tensor fields defined in terms of the second fundamental form by means of arbitrary tensor operations and submanifolds on which the matching tensor fields are parallel is completely solved in spaces of constant curvature, in terms of various classes of envelopes
[en] The one-loop divergences are calculated for the recently proposed ghost-free massive gravity model, where the action depends on both metric and external tensor field f. The non-polynomial structure of the massive term is reduced to a more standard form by means of auxiliary tensor field, which is settled on-shell after quantum calculations are performed. As one should expect, the counter-terms do not reproduce the form of the classical action. Moreover, the result has the form of the power series in f.
[en] A Fourier space formalism based on the shape amplitude of a particle is used to compute the demagnetization tensor field for uniformly magnetized particles of arbitrary shape. We provide a list of explicit shape amplitudes for important particle shapes, among others: the sphere, the cylindrical tube, an arbitrary polyhedral shape, a truncated paraboloid, and a cone truncated by a spherical cap. In Part I of this two-part paper, an analytical representation of the demagnetization tensor field for particles with cylindrical symmetry is provided, as well as expressions for the magnetostatic energy and the volumetric demagnetization factors
[en] We consider all possible finite representations of the Lorentz group and their association with the spin properties of the particles. It is shown that, for a given nontrivial spin, there exist several nonequivalent representations differing in chirality, which in the massless case correspond to different particles with different helicities. A spin-1 case, which includes the standard field description by the vector-potential and a non-standard one by the second rank antisymmetric tensor field, is considered in detail. The first field transforms under the real representation (1/2,1/2), while the second one does so under the chiral representations (1,0) and (0,1). By considering spin-1 hadron resonances as an example, it is shown that these two fields describe two different types of particles existing in nature. This idea is further applied to the construction of the Standard Model extension using a new type of spin-1 chiral particles. Its phenomenological consequences are studied in detail.
[en] Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial cases are considered. (author)