1,844 research outputs found
Translation-invariant generalized topologies induced by probabilistic norms
In this paper we consider probabilistic normed spaces as defined by Alsina,
Sklar, and Schweizer, but equipped with non necessarily continuous triangle
functions. Such spaces endow a generalized topology that is
Fr\'echet-separable, translation-invariant and countably generated by radial
and circled 0-neighborhoods. Conversely, we show that such generalized
topologies are probabilistically normable.Comment: 8 pages. Some minor changes and corrections have been mad
On the connections between Skyrme and Yang Mills theories
Skyrme theories on S^3 and S^2, are analyzed using the generalized zero
curvature in any dimensions. In the first case, new symmetries and integrable
sectors, including the B =1 skyrmions, are unraveled. In S^2 the relation to
QCD suggested by Faddeev is discussedComment: Talk at the Workshop on integrable theories, solitons and duality.
IFT Sao Paulo July 200
Tau-functions and Dressing Transformations for Zero-Curvature Affine Integrable Equations
The solutions of a large class of hierarchies of zero-curvature equations
that includes Toda and KdV type hierarchies are investigated. All these
hierarchies are constructed from affine (twisted or untwisted) Kac-Moody
algebras~. Their common feature is that they have some special ``vacuum
solutions'' corresponding to Lax operators lying in some abelian (up to the
central term) subalgebra of~; in some interesting cases such subalgebras
are of the Heisenberg type. Using the dressing transformation method, the
solutions in the orbit of those vacuum solutions are constructed in a uniform
way. Then, the generalized tau-functions for those hierarchies are defined as
an alternative set of variables corresponding to certain matrix elements
evaluated in the integrable highest-weight representations of~. Such
definition of tau-functions applies for any level of the representation, and it
is independent of its realization (vertex operator or not). The particular
important cases of generalized mKdV and KdV hierarchies as well as the abelian
and non abelian affine Toda theories are discussed in detail.Comment: 27 pages, plain Te
Critical failure of the principle equivalence between acceleration and gravity
The principle of equivalence between acceleration and gravity of general relativity is reviewed in a thought experiment of two bodies, aligned according to the perpendicular, under the reciprocal action of their gravity, in free fall, inside of an uniformly accelerated reference system, in the vacuum. The result is that the two bodies fall with a different acceleration. This result invalidates such principle
Bringing Together Gravity and the Quanta
Due to its underlying gauge structure, teleparallel gravity achieves a
separation between inertial and gravitational effects. It can, in consequence,
describe the isolated gravitational interaction without resorting to the
equivalence principle, and is able to provide a tensorial definition for the
energy-momentum density of the gravitational field. Considering the conceptual
conflict between the local equivalence principle and the nonlocal uncertainty
principle, the replacement of general relativity by its teleparallel equivalent
can be considered an important step towards a prospective reconciliation
between gravitation and quantum mechanics.Comment: 9 pages. Contribution to the proceedings of the Albert Einstein
Century International Conference, Paris, 18-22 July, 200
- …