5,687 research outputs found
Dimensional curvature identities on pseudo-Riemannian geometry
The curvature tensor of a pseudo-Riemannian metric, and its covariant
derivatives, satisfy certain identities that hold on any manifold of dimension
less or equal than .
In this paper, we re-elaborate recent results by Gilkey-Park-Sekigawa
regarding -covariant dimensional curvature identities, for . To this
end, we use the classical theory of natural operations, that allows us to
simplify some arguments and to generalize the description of
Gilkey-Park-Sekigawa.
Thus, our main result describes the first space of -covariant dimensional
curvature identities, for any even .Comment: Polished version. 15 page
Automorphisms of classical geometries in the sense of Klein
In this note, we compute the group of automorphisms of Projective, Affine and
Euclidean Geometries in the sense of Klein.
As an application, we give a simple construction of the outer automorphism of
S_6.Comment: 8 page
Lovelock's theorem revisited
Let (X, g) be an arbitrary pseudo-riemannian manifold. A celebrated result by
Lovelock gives an explicit description of all second-order natural
(0,2)-tensors on X, that satisfy the conditions of being symmetric and
divergence-free. Apart from the dual metric, the Einstein tensor of g is the
simplest example.
In this paper, we give a short and self-contained proof of this theorem,
simplifying the existing one by formalizing the notion of derivative of a
natural tensor.Comment: 9 page
Running gravitational couplings, decoupling, and curved spacetime renormalization
We propose to slightly generalize the DeWitt-Schwinger adiabatic
renormalization subtractions in curved space to include an arbitrary
renormalization mass scale . The new predicted running for the
gravitational couplings are fully consistent with decoupling of heavy massive
fields. This is a somewhat improvement with respect to the more standard
treatment of minimal (DeWitt-Schwinger) subtractions via dimensional
regularization. We also show how the vacuum metamorphosis model emerges from
the running couplings.Comment: Some points clarified, misprints corrected; to appear in Phys. Rev.
Running couplings from adiabatic regularization
We extend the adiabatic regularization method by introducing an arbitrary
mass scale in the construction of the subtraction terms. This allows us
to obtain, in a very robust way, the running of the coupling constants by
demanding -invariance of the effective semiclassical (Maxwell-Einstein)
equations. In particular, we get the running of the electric charge of
perturbative quantum electrodynamics. Furthermore, the method brings about a
renormalization of the cosmological constant and the Newtonian gravitational
constant. The running obtained for these dimensionful coupling constants has
new relevant (non-logarithmic) contributions, not predicted by dimensional
regularization.Comment: Revised version. Some points clarified. New references added. 6
pages. To appear in Phys. Lett.
Applications of Intuitionistic Logic in Answer Set Programming
We present some applications of intermediate logics in the field of Answer
Set Programming (ASP). A brief, but comprehensive introduction to the answer
set semantics, intuitionistic and other intermediate logics is given. Some
equivalence notions and their applications are discussed. Some results on
intermediate logics are shown, and applied later to prove properties of answer
sets. A characterization of answer sets for logic programs with nested
expressions is provided in terms of intuitionistic provability, generalizing a
recent result given by Pearce.
It is known that the answer set semantics for logic programs with nested
expressions may select non-minimal models. Minimal models can be very important
in some applications, therefore we studied them; in particular we obtain a
characterization, in terms of intuitionistic logic, of answer sets which are
also minimal models. We show that the logic G3 characterizes the notion of
strong equivalence between programs under the semantic induced by these models.
Finally we discuss possible applications and consequences of our results. They
clearly state interesting links between ASP and intermediate logics, which
might bring research in these two areas together.Comment: 30 pages, Under consideration for publication in Theory and Practice
of Logic Programmin
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