13,904 research outputs found
Clifford Valued Differential Forms, and Some Issues in Gravitation, Electromagnetism and 'Unified' Theories
In this paper we show how to describe the general theory of a linear metric
compatible connection with the theory of Clifford valued differential forms.
This is done by realizing that for each spacetime point the Lie algebra of
Clifford bivectors is isomorphic to the Lie algebra of Sl(2,C). In that way the
pullback of the linear connection under a local trivialization of the bundle
(i.e., a choice of gauge) is represented by a Clifford valued 1-form. That
observation makes it possible to realize immediately that Einstein's
gravitational theory can be formulated in a way which is similar to a Sl(2,C)
gauge theory. Such a theory is compared with other interesting mathematical
formulations of Einstein's theory. and particularly with a supposedly "unified"
field theory of gravitation and electromagnetism proposed by M. Sachs. We show
that his identification of Maxwell equations within his formalism is not a
valid one. Also, taking profit of the mathematical methods introduced in the
paper we investigate a very polemical issue in Einstein gravitational theory,
namely the problem of the 'energy-momentum' conservation. We show that many
statements appearing in the literature are confusing or even wrong.Comment: Misprints and errors in some equations of the printed version have
been correcte
Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics
We revisit the Mittag-Leffler functions of a real variable , with one, two
and three order-parameters , as far as their Laplace
transform pairs and complete monotonicty properties are concerned. These
functions, subjected to the requirement to be completely monotone for ,
are shown to be suitable models for non--Debye relaxation phenomena in
dielectrics including as particular cases the classical models referred to as
Cole-Cole, Davidson-Cole and Havriliak-Negami. We show 3D plots of the response
functions and of the corresponding spectral distributions, keeping fixed one of
the three order-parameters.Comment: 22 pages, 6 figures, Second Revised Versio
- …