6,254 research outputs found
The Theory of Kairons
In relativistic quantum mechanics wave functions of particles satisfy field
equations that have initial data on a space--like hypersurface. We propose a
dual field theory of ``wavicles'' that have their initial data on a time--like
worldline. Propagation of such fields is superluminal, even though the Hilbert
space of the solutions carries a unitary representation of the Poincare group
of mass zero. We call the objects described by these field equations
``Kairons''. The paper builds the field equations in a general relativistic
framework, allowing for a torsion. Kairon fields are section of a vector bundle
over space-time. The bundle has infinite--dimensional fibres.Comment: Latex, 21 pages, 1 figure, several misprints from the previous
version correcte
Hermitian metrics on F-manifolds
An -manifold is complex manifold with a multiplication on the holomorphic
tangent bundle with a certain integrability condition. Important examples are
Frobenius manifolds and especially base spaces of universal unfoldings of
isolated hypersurface singularities. This paper reviews the construction of
hermitian metrics on -manifolds from geometry. It clarifies the logic
between several notions. It also introduces a new {\it canonical} hermitian
metric. Near irreducible points it makes the manifold almost hyperbolic. This
holds for the singularity case and will hopefully lead to applications there.Comment: 2nd version 36 pages. Compared to the 1st version (32 pages), the
sections 2.4 and 2.5 have been extende
POINTLESS SPACES IN GENERAL RELATIVITY
The new approach to quantize the gravity based on the notion of differential
algebra is suggested. It is shown that the differential geometry of this object
can not be described in terms of points. The spatialization procedure giving
rise to points by loosing a part of the entire structure is discussed. The
counterpart of the traditional objects of differential geometry are studied.Comment: 40 Kb, latex, no figures, paper accepted for publication in the
International Journal of Theoretical Physics (May 1995
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