24,781 research outputs found
Cauchy Type Integrals of Algebraic Functions
We consider Cauchy type integrals with an algebraic function. The main goal is to give
constructive (at least, in principle) conditions for to be an algebraic
function, a rational function, and ultimately an identical zero near infinity.
This is done by relating the Monodromy group of the algebraic function , the
geometry of the integration curve , and the analytic properties of the
Cauchy type integrals. The motivation for the study of these conditions is
provided by the fact that certain Cauchy type integrals of algebraic functions
appear in the infinitesimal versions of two classical open questions in
Analytic Theory of Differential Equations: the Poincar\'e Center-Focus problem
and the second part of the Hilbert 16-th problem.Comment: 58 pages, 19 figure
Computer theorem proving in math
We give an overview of issues surrounding computer-verified theorem proving
in the standard pure-mathematical context. This is based on my talk at the PQR
conference (Brussels, June 2003)
New Constructions in Local Quantum Physics
Among several ideas which arose as consequences of modular localization there
are two proposals which promise to be important for the classification and
construction of QFTs. One is based on the observation that wedge-localized
algebras may have particle-like generators with simple properties and the
second one uses the structural simplification of wedge algebras in the
holographic lightfront projection. Factorizable d=1+1 models permit to analyse
the interplay between particle-like aspects and chiral field properties of
lightfront holography. Pacs 11.10.-z, 11.55.-mComment: 21 pages, conference report, references adde
A Manifestly Gauge-Invariant Approach to Quantum Theories of Gauge Fields
In gauge theories, physical histories are represented by space-time
connections modulo gauge transformations. The space of histories is thus
intrinsically non-linear. The standard framework of constructive quantum field
theory has to be extended to face these {\it kinematical} non-linearities
squarely. We first present a pedagogical account of this problem and then
suggest an avenue for its resolution.Comment: 27 pages, CGPG-94/8-2, latex, contribution to the Cambridge meeting
proceeding
Integrals and Valuations
We construct a homeomorphism between the compact regular locale of integrals
on a Riesz space and the locale of (valuations) on its spectrum. In fact, we
construct two geometric theories and show that they are biinterpretable. The
constructions are elementary and tightly connected to the Riesz space
structure.Comment: Submitted for publication 15/05/0
Quantum Field Theory: Where We Are
We comment on the present status, the concepts and their limitations, and the
successes and open problems of the various approaches to a relativistic quantum
theory of elementary particles, with a hindsight to questions concerning
quantum gravity and string theory.Comment: To appear in: An Assessment of Current Paradigms in the Physics of
Fundamental Phenomena, to be published by Springer Verlag (2006
- …