Browsing by Author "Reyes, Enrique G."

Now showing 1 - 4 of 4
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    Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras
    (2017) Beltran, Jarnishs; Farinati, Marco; Reyes, Enrique G.
    We describe the space of central extensions of the associative algebra Ψn of formal pseudo-differential symbols in n≥1 independent variables using Hochschild (co)homology groups: we prove that the first Hochschild (co)homology group HH1(Ψn) is 2n-dimensional and we use this fact to calculate the first Lie (co)homology group HLie1(Ψn) of Ψn equipped with the Lie bracket induced by its associative algebra structure. As an application, we use our calculations to provide examples of infinite-dimensional quadratic symplectic Lie algebras.
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    From Hopf fibrations to exotic causal replacements
    (2016) Bezares, Miguel; Goulart, Erico; Palomera, Gonzalo; Pons, Daniel J.; Reyes, Enrique G.
    Topological solitons are relevant in several areas of physics. Recently, these configurations have been investigated in contexts as diverse as hydrodynamics, Bose-Einstein condensates, ferromagnetism, knotted light and non-Abelian gauge theories. In this paper we address the issue of wave propagation about a static Hopf soliton in the context of the Nicole model. Working within the geometrical optics limit, we show that several nontrivial lensing effects emerge due to nonlinear interactions as long as the theory remains hyperbolic. We conclude that similar effects are very likely to occur in effective field theories characterized by a topological invariant such as the Skyrme model of pions.
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    The Ehlers–Geroch theorem on geodesic motion in general relativity
    (2015) Bezares, Miguel; Palomera, Gonzalo; Pons, Daniel J.; Reyes, Enrique G.
    We provide a detailed and rigorous proof of (a generalized version of) the Ehlers–Geroch theorem on geodesic motion in metric theories of gravity: we assume that (M, g) is a spacetime satisfying an averaged form of the dominant energy condition and some further technical assumptions indicated in the bulk of this paper. Then, a small body which is allowed to deform the original spacetime metric g moves, nonetheless, along a geodesic of (M, g).

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