Mathisson's helical motions for a spinning particle --- are they unphysical?

It has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descriptions of the motion of a spinning body, the difference between them being the choice of the representative point of the particle, thus a gauge choice. We discuss the kinematical explanation of these motions, and we dynamically interpret them through the concept of hidden momentum. We also show that, contrary to previous claims, the frequency of the helical motions coincides, even in the relativistic limit, with the zitterbewegung frequency of the Dirac equation for the electron

Busca de inibidores da enzima glicossomal gliceraldeído 3-fosfato desidrogenase de Trypanosoma cruzi

The inhibitory activity of crude extracts of Meliaceae and Rutaceae plants on glycosomal glyceraldehyde-3-phosphate dehydrogenase (gGAPDH) enzyme from Trypanosoma cruzi was evaluated at 100 μg/mL. Forty-six extracts were tested and fifteen of them showed significant inhibitory activity (IA % > 50). The majority of the assayed extracts of Meliaceae plants (Cedrela fissilis, Cipadessa fruticosa and Trichilia ramalhoi) showed high ability to inhibit the enzymatic activity. The fractionation of the hexane extract from branches of C. fruticosa led to the isolation of three flavonoids: flavone, 7-methoxyflavone and 3',4',5',5,7-pentamethoxyflavone. The two last compounds showed high ability to inhibit the gGAPDH activity. Therefore, the assayed Meliaceae species could be considered as a promising source of lead compounds against Chagas' disease.Nesse trabalho foi avaliada a atividade inibitória sobre a enzima glicossomal gliceraldeído-3-fosfato desidrogenase de T. cruzi (gGAPDH) de extratos vegetais oriundos de plantas das famílias Meliaceae e Rutaceae, na concentração de 100 μg/mL. Foram testados 46 extratos, dos quais 15 apresentaram atividade inibitória significativa (% AI > 50). A maioria dos extratos de plantas da família Meliaceae (Cedrela fissilis, Cipadessa fruticosa e Trichilia ramalhoi) apresentou grande potencial em inibir a atividade enzimática. O fracionamento do extrato hexânico dos galhos de C. fruticosa permitiu o isolamento de três flavonóides: flavona, 7-metoxiflavona e 3',4',5',5,7-pentametoxiflavona. Os dois últimos foram ativos na inibição da atividade de gGAPDH. Desta forma, as três espécies de Meliaceae testadas podem ser consideradas promissoras na busca de compostos protótipos para o controle da doença de Chagas.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Ensino Superior (CAPES)FINEP - Financiadora de Estudos e Projeto

Spacetime dynamics of spinning particles - exact electromagnetic analogies

We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the following analogous setups: magnetic dipoles in the field of non-spinning/spinning charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter spacetimes. The implications of the time projections of the tidal tensors are illustrated by the work done on the particle in various frames; in particular, a reciprocity is found to exist: in a frame comoving with the particle, the electromagnetic (but not the gravitational) field does work on it, causing a variation of its proper mass; conversely, for "static observers," a stationary gravitomagnetic (but not a magnetic) field does work on the particle, and the associated potential energy is seen to embody the Hawking-Wald spin-spin interaction energy. The issue of hidden momentum, and its counterintuitive dynamical implications, is also analyzed. Finally, a number of issues regarding the electromagnetic interaction and the physical meaning of Dixon's equations are clarified.Comment: 32+11 pages, 5 figures. Edited and further improved version, with new Section C.2 unveiling analogies for arbitrary spin conditions, and new Sec. 3.2.3 in the Supplement making connection to the post-Newtonian approximation; former Sec. III.B.4 and Appendix C moved to the (reshuffled) Supplement; references updated. The Supplement is provided in ancillary file. Matches the final published versio

Bi-conformal vector fields and their applications

We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric \G to be scaled by different conformal factors. In particular, we study their infinitesimal version, called bi-conformal vector fields. We show the differential conditions characterizing them in terms of a "square root" of the metric, or equivalently of two complementary orthogonal projectors. Keeping these fixed, the set of bi-conformal vector fields is a Lie algebra which can be finite or infinite dimensional according to the dimensionality of the projectors. We determine (i) when an infinite-dimensional case is feasible and its properties, and (ii) a normal system for the generators in the finite-dimensional case. Its integrability conditions are also analyzed, which in particular provides the maximum number of linearly independent solutions. We identify the corresponding maximal spaces, and show a necessary geometric condition for a metric tensor to be a double-twisted product. More general ``breakable'' spaces are briefly considered. Many known symmetries are included, such as conformal Killing vectors, Kerr-Schild vector fields, kinematic self-similarity, causal symmetries, and rigid motions.Comment: Replaced version with some changes in the terminology and a new theorem. To appear in Classical and Quantum Gravit

Gravito-electromagnetic analogies

We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial fields from the so-called "1+3 formalism", and the analogy based on tidal tensors. Both are reformulated, extended and generalized. We write in both formalisms the Maxwell and the full exact Einstein field equations with sources, plus the algebraic Bianchi identities, which are cast as the source-free equations for the gravitational field. New results within each approach are unveiled. The well known analogy between linearized gravity and electromagnetism in Lorentz frames is obtained as a limiting case of the exact ones. The formal analogies between the Maxwell and Weyl tensors are also discussed, and, together with insight from the other approaches, used to physically interpret gravitational radiation. The precise conditions under which a similarity between gravity and electromagnetism occurs are discussed, and we conclude by summarizing the main outcome of each approach.Comment: 60 pages, 2 figures. Improved version (compared to v2) with some re-write, notation improvements and a new figure that match the published version; expanded compared to the published version to include Secs. 2.3 and

Activities of extracts and compounds from Spiranthera odoratissima St. Hil. (Rutaceae) in leaf-cutting ants and their symbiotic fungus

The study of the Spiranthera odoratissima St. Hil (Rutaceae) branches extracts led to the isolation of the furoquinoline (dictamine, gamma-fagarine and skimmianine) and 2-arylquinoli-4-one (1-methyl-2-phenylquinolin-4-one) alkaloids and limonoids (limonexic acid and limonin). The compounds 1-methyl-2-phenylquinolin-4-one and limonexic acid were isolated for the first time from the Spiranthera. These furoquinoline and 2-arylquinoli-4-one alkaloids and limonoids showed insecticidal and/or fungicidal activity in the nest of the Atta sexdens rubropilosa