Conformal invariance and rationality in an even dimensional quantum field theory

Invariance under finite conformal transformations in Minkowski space and the Wightman axioms imply strong locality (Huygens principle) and rationality of correlation functions, thus providing an extension of the concept of vertex algebra to higher dimensions. Gibbs (finite temperature) expectation values appear as elliptic functions in the conformal time. We survey and further pursue our program of constructing a globally conformal invariant model of a hermitean scalar field L of scale dimension four in Minkowski space-time which can be interpreted as the Lagrangian density of a gauge field theory.Comment: 33 pages, misprints corrected, references update

Renormalization of Massless Feynman Amplitudes in Configuration Space

A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration space. For a massless quantum field theory (QFT) we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincare covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences - i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal - we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary - not necessarily primitively divergent - Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.Comment: LaTeX, 64 page

Rationality of conformally invariant local correlation functions on compactified Minkowski space

Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification of Minkowski space and yields a strong form of locality valid for all non-isotropic intervals if assumed true for space-like separations.Comment: 20 pages, LATEX, amsfonts, latexsy

Configuration Space Renormalization of Massless QFT as an Extension Problem for Associate Homogeneous Distributions

Con guration (x-)space renormalization of euclidean Green functions in a massless quantum eld theory is reduced (by generalizing Hörmander's approach [H]) to the study of extensions of associate homogeneous distributions. Primitively divergent graphs are renormalized, in particular, by subtracting the residue of an analytically regularized expression. The renormalized Green functions are again associate homogeneous distributions that transform under indecomposable representations of the dilation group

Smartbook: Semantics Inside

This paper presents a vision for the future of the e-books which entails further development of technologies that will facilitate the creation and use of a new generation of "smart" books: e-books that are evolving, highly interactive, customisable, adaptable, intelligent, and furnished with a rich set of collaborative authoring and reading support services. The proposed set of tools will be integrated into an intelligent framework for collaborative book authoring and experiencing called SmartBook. The paper promotes the idea that the semantic technologies, intensively developed recently in connection with the Semantic Web initiative, can be incorporated in the book and become the key factor of making it "smarter"

SmartBook – the future E-book and educatonal hypermedia

Доклад по покана, поместен в сборника на Националната конференция "Образованието в информационното общество", Пловдив, май, 2009This paper presents a vision for the future of the e-books as part of the growing collective intelligence. The vision entails further development of technologies that will facilitate the creation and use of a new generation of ‘smart’ books: e-books that are evolving, highly interactive, customisable, adaptable, intelligent, and furnished with a rich set of collaborative authoring and reading support services. The proposed set of tools will be integrated into an intelligent framework for collaborative book authoring and experiencing called SmartBook. The paper also discusses the opportunities to use SmartBook as a educational hypermedia.Асоциация "Развитие на информационното общество", Институт по математика и информатика при БАН, Пловдивски университе

Infinite dimensional Lie algebras in 4D conformal quantum field theory

The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, V_m(x,y), where the m span a finite dimensional real matrix algebra M closed under transposition. The associative algebra M is irreducible iff its commutant M' coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite dimensional Lie algebra: a central extension of sp(infty,R) corresponding to the field R of reals, of u(infty,infty) associated to the field C of complex numbers, and of so*(4 infty) related to the algebra H of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N), and U(N,H)=Sp(2N), respectively.Comment: 16 pages, with minor improvements as to appear in J. Phys.

Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields

The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective gauge groups U(N) and O(N) confirms the expectations based on general results obtained in the framework of local nets in algebraic quantum field theory, but the approach using standard Lie algebra methods rather than abstract duality theory is complementary. The result indicates that one does not lose interesting models if one postulates the absence of scalar fields of dimension D-2 in models with global conformal invariance. Another remarkable outcome is the observation that, with an appropriate choice of the Hamiltonian, a Lie algebra embedded into the associative algebra of observables completely fixes the representation theory.Comment: 27 pages, v3: result improved by eliminating redundant assumptio