2,430,665 research outputs found

    Vector theories in cosmology

    Get PDF
    This article provides a general study of the Hamiltonian stability and the hyperbolicity of vector field models involving both a general function of the Faraday tensor and its dual, f(F2,FF~)f(F^2,F\tilde F), as well as a Proca potential for the vector field, V(A2)V(A^2). In particular it is demonstrated that theories involving only f(F2)f(F^2) do not satisfy the hyperbolicity conditions. It is then shown that in this class of models, the cosmological dynamics always dilutes the vector field. In the case of a nonminimal coupling to gravity, it is established that theories involving Rf(A2)R f(A^2) or Rf(F2)Rf(F^2) are generically pathologic. To finish, we exhibit a model where the vector field is not diluted during the cosmological evolution, because of a nonminimal vector field-curvature coupling which maintains second-order field equations. The relevance of such models for cosmology is discussed.Comment: 17 pages, no figur

    Generalization of a criterion for semistable vector bundles

    Get PDF
    It is known that a vector bundle E on a smooth projective curve Y defined over an algebraically closed field is semistable if and only if there is a vector bundle F on Y such that the cohomologies of E\otimes F vanish. We extend this criterion for semistability to vector bundles on curves defined over perfect fields. Let X be a geometrically irreducible smooth projective curve defined over a perfect field k, and let E be a vector bundle on X. We prove that E is semistable if and only if there is a vector bundle F on XX such that the cohomologies of E\otimes F vanish. We also give an explicit bound for the rank of FF

    The model theory of Commutative Near Vector Spaces

    Full text link
    In this paper we study near vector spaces over a commutative FF from a model theoretic point of view. In this context we show regular near vector spaces are in fact vector spaces. We find that near vector spaces are not first order axiomatisable, but that finite block near vector spaces are. In the latter case we establish quantifier elimination, and that the theory is controlled by which elements of the pointwise additive closure of FF are automorphisms of the near vector space

    ∞\infty-jets of difeomorphisms preserving orbits of vector fields

    Full text link
    Let FF be a smooth vector field defined in a neighborhood of the origin in Rn\mathbb{R}^n, F(O)=0F(O)=0, and let FtF_t be its local flow. Denote by EE the set of germs of diffeomorphisms h:Rn→Rnh:\mathbb{R}^n \to \mathbb{R}^n preserving orbits of FF and let EidrE_{\mathrm{id}}^r be the identity component of EE with respect to CrC^r-topology. Then every EidrE_{\mathrm{id}}^{r} contains a subset ShSh consisting of mappings of the form Ff(x)(x)F_{f(x)}(x), where f:Rn→Rf: \mathbb{R}^n \to \mathbb{R} is a smooth function. It was proved earlier by the author that if FF is a linear vector field, then Sh=Eid0Sh=E_{\mathrm{id}}^0. In this paper we present a class of vector fields for which ShSh and Eid1E_{\mathrm{id}}^1 coincide on the level of ∞\infty-jets. We also establish a parameter rigidity of linear vector fields and "reduced" Hamiltonian vector fields of real homogeneous polynomials in two variables.Comment: 34 pages. version 5. Many misprints are corrected and some minor changes are mad
    • …
    corecore