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

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

New methods in conformal partial wave analysis

We report on progress concerning the partial wave analysis of higher correlation functions in conformal quantum field theory.Comment: 16 page

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

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.

Measuring Online Social Bubbles

Social media have quickly become a prevalent channel to access information, spread ideas, and influence opinions. However, it has been suggested that social and algorithmic filtering may cause exposure to less diverse points of view, and even foster polarization and misinformation. Here we explore and validate this hypothesis quantitatively for the first time, at the collective and individual levels, by mining three massive datasets of web traffic, search logs, and Twitter posts. Our analysis shows that collectively, people access information from a significantly narrower spectrum of sources through social media and email, compared to search. The significance of this finding for individual exposure is revealed by investigating the relationship between the diversity of information sources experienced by users at the collective and individual level. There is a strong correlation between collective and individual diversity, supporting the notion that when we use social media we find ourselves inside "social bubbles". Our results could lead to a deeper understanding of how technology biases our exposure to new information