164 research outputs found
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
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
Reconstruction of a vertex algebra in higher dimensions from its one-dimensional restriction
Vertex algebras in higher dimensions correspond to models of quantum field
theory with global conformal invariance. Any vertex algebra in higher
dimensions admits a restriction to a vertex algebra in any lower dimension, and
in particular, to dimension one. In this paper, we find natural conditions
under which the converse passage is possible. These conditions include a
unitary action of the conformal Lie algebra with a positive energy, which is
given by local endomorphisms and obeys certain integrability properties.Comment: 25 pages; v2 fixed typos and expanded some proofs; v3 improved the
expositio
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
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