755 research outputs found
A Lorentzian Quantum Geometry
We propose a formulation of a Lorentzian quantum geometry based on the
framework of causal fermion systems. After giving the general definition of
causal fermion systems, we deduce space-time as a topological space with an
underlying causal structure. Restricting attention to systems of spin dimension
two, we derive the objects of our quantum geometry: the spin space, the tangent
space endowed with a Lorentzian metric, connection and curvature. In order to
get the correspondence to differential geometry, we construct examples of
causal fermion systems by regularizing Dirac sea configurations in Minkowski
space and on a globally hyperbolic Lorentzian manifold. When removing the
regularization, the objects of our quantum geometry reduce precisely to the
common objects of Lorentzian spin geometry, up to higher order curvature
corrections.Comment: 65 pages, LaTeX, 4 figures, many small improvements (published
version
The stress energy tensor of a locally supersymmetric quantum field on a curved spacetime
For an analogon of the free Wess-Zumino model on Ricci flat spacetimes, the
relation between a conserved `supercurrent' and the point-separated improved
energy momentum tensor is investigated and a similar relation as on Minkowski
space is established. The expectation value of the latter in any globally
Hadamard product state is found to be a priori finite in the coincidence limit
if the theory is massive. On arbitrary globally hyperbolic spacetimes the
`supercurrent' is shown to be a well defined operator valued distribution on
the GNS Hilbertspace of any globally Hadamard product state. Viewed as a new
field, all n-point distributions exist, giving a new example for a Wightman
field on that manifold. Moreover, it is shown that this field satisfies a new
wave front set spectrum condition in a non trivial way.Comment: 100 pages, PhD Thesis, LaTeX2e + AMS-LaTeX, 5 figures appended as
uuencoded ps-file
Trace-class approach in scattering problems for perturbations of media
We consider the operators and
where and are positively definite bounded matrix-valued
functions and is an elliptic differential operator. Our main result is
that the wave operators for the pair , exist and are complete if the
difference , , as . Our
point is that no special assumptions on are required. Similar results
are obtained in scattering theory for the wave equation.Comment: 11 page
Computation of Generalized Averaged Gaussian Quadrature Rules
The estimation of the quadrature error of a Gauss quadrature rule when applied to the
approximation of an integral determined by a real-valued integrand and a real-valued
nonnegative measure with support on the real axis is an important problem in scientific
computing. Laurie [2] developed anti-Gauss quadrature rules as an aid to estimate this error.
Under suitable conditions the Gauss and associated anti-Gauss rules give upper and lower
bounds for the value of the desired integral. It is then natural to use the average of
Gauss and anti-Gauss rules as an improved approximation of the integral. Laurie also
introduced these averaged rules. More recently, the author derived new averaged Gauss
quadrature rules that have higher degree of exactness for the same number of nodes as the
averaged rules proposed by Laurie. In [2], [5], [3] stable numerical procedures for
computation of the corresponding averaged Gaussian rules are proposed. An analogous
procedure can be applied also for a more general class of weighted averaged Gaussian rules
introduced in [1]. Those results are presented in [4]. Here we we give a survey of the quoted
results, which are obtained jointly with L. Reichel (Kent State Univ., OH (U.S.)
Mixed Variational Inequality Interval-valued Problem: Theorems of Existence of Solutions
In this article, our efforts focus on finding the conditions for the existence of solutions of Mixed Stampacchia Variational Inequality Interval-valued Problem on Hadamard manifolds with monotonicity assumption by using KKM mappings. Conditions that allow us to prove the existence of equilibrium points in a market of perfect competition. We will identify solutions of Stampacchia variational problem and optimization problem with the interval-valued convex objective function, improving on previous results in the literature. We will illustrate the main results obtained with some examples and numerical results
Integral Transformation, Operational Calculus and Their Applications
The importance and usefulness of subjects and topics involving integral transformations and operational calculus are becoming widely recognized, not only in the mathematical sciences but also in the physical, biological, engineering and statistical sciences. This book contains invited reviews and expository and original research articles dealing with and presenting state-of-the-art accounts of the recent advances in these important and potentially useful subjects
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