2,955 research outputs found
Semi-indefinite-inner-product and generalized Minkowski spaces
In this paper we parallelly build up the theories of normed linear spaces and
of linear spaces with indefinite metric, called also Minkowski spaces for
finite dimensions in the literature.
In the first part of this paper we collect the common properties of the semi-
and indefinite-inner-products and define the semi-indefinite-inner-product and
the corresponding structure, the semi-indefinite-inner-product space. We give a
generalized concept of Minkowski space embedded in a
semi-indefinite-inner-product space using the concept of a new product, that
contains the classical cases as special ones.
In the second part of this paper we investigate the real, finite dimensional
generalized Minkowski space and its sphere of radius . We prove that it can
be regarded as a so-called Minkowski-Finsler space and if it is homogeneous one
with respect to linear isometries, then the Minkowski-Finsler distance its
points can be determined by the Minkowski-product
Nuclearity, Local Quasiequivalence and Split Property for Dirac Quantum Fields in Curved Spacetime
We show that a free Dirac quantum field on a globally hyperbolic spacetime
has the following structural properties: (a) any two quasifree Hadamard states
on the algebra of free Dirac fields are locally quasiequivalent; (b) the
split-property holds in the representation of any quasifree Hadamard state; (c)
if the underlying spacetime is static, then the nuclearity condition is
satisfied, that is, the free energy associated with a finitely extended
subsystem (``box'') has a linear dependence on the volume of the box and goes
like for large temperatures , where is the number of
dimensions of the spacetime.Comment: Latex, 33 pages, no figures. v3: Corrections to the proofs of thm.
4.1 and thm. 3.1 and more reference
Paired accelerated arames: The perfect interferometer with everywhere smooth wave amplitudes
Rindler's acceleration-induced partitioning of spacetime leads to a
nature-given interferometer. It accomodates quantum mechanical and wave
mechanical processes in spacetime which in (Euclidean) optics correspond to
wave processes in a ``Mach-Zehnder'' interferometer: amplitude splitting,
reflection, and interference. These processes are described in terms of
amplitudes which behave smoothly across the event horizons of all four Rindler
sectors. In this context there arises quite naturally a complete set of
orthonormal wave packet histories, one of whose key properties is their
"explosivity index". In the limit of low index values the wave packets trace
out fuzzy world lines. By contrast, in the asymptotic limit of high index
values, there are no world lines, not even fuzzy ones. Instead, the wave packet
histories are those of entities with non-trivial internal collapse and
explosion dynamics. Their details are described by the wave processes in the
above-mentioned Mach-Zehnder interferometer. Each one of them is a double slit
interference process. These wave processes are applied to elucidate the
amplification of waves in an accelerated inhomogeneous dielectric. Also
discussed are the properties and relationships among the transition amplitudes
of an accelerated finite-time detector.Comment: 38 pages, RevTex, 10 figures, 4 mathematical tutorials. Html version
of the figures and of related papers available at
http://www.math.ohio-state.edu/~gerlac
Notes on Yang-Mills--Higgs monopoles and dyons on R^D, and Chern-Simons--Higgs solitons on \R^{D-2}: Dimensional reduction of Chern-Pontryagin densities
We review work on construction of Monopoles in higher dimensions. These are
solutions to a particular class of models descending from Yang--Mills systems
on even dimensional bulk, with Spheres as codimensions. The topological lower
bounds on the Yang-Mills action translate to Bogomol'nyi lower bounds on the
residual Yang-Mills-Higgs systems. Mostly, consideration is restricted to 8
dimensional bulk systems, but extension to the arbitrary case follows
systematically. After presenting the monopoles, the corresponding dyons are
also constructed. Finally, new Chern-Simons densities expressed in terms of
Yang-Mills and Higgs fields are presented. These are defined in all dimensions,
including in even dimensional spacetimes. They are constructed by subjecting
the dimensionally reduced Chern-Pontryagin densites to further descent by two
steps.Comment: 50 pages, no figures. Revised and extended final versio
On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets
Summarizing basic facts from abstract topological modules over Colombeau
generalized complex numbers we discuss duality of Colombeau algebras. In
particular, we focus on generalized delta functionals and operator kernels as
elements of dual spaces. A large class of examples is provided by
pseudodifferential operators acting on Colombeau algebras. By a refinement of
symbol calculus we review a new characterization of the wave front set for
generalized functions with applications to microlocal analysis
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