Conformal generally covariant quantum field theory: The scalar field and its Wick products

Simple item page
dc.creatorPinamonti, Nicola
dc.date2008-06-04
dc.date2009-02-03
dc.date.accessioned2026-07-07T13:13:18Z
dc.date.available2026-07-07T13:13:18Z
dc.descriptionIn this paper we generalize the construction of generally covariant quantum theories given in the work of Brunetti, Fredenhagen and Verch to encompass the conformal covariant case. After introducing the abstract framework, we discuss the massless conformally coupled Klein Gordon field theory, showing that its quantization corresponds to a functor between two certain categories. At the abstract level, the ordinary fields, could be thought as natural transformations in the sense of category theory. We show that, the Wick monomials without derivatives (Wick powers), can be interpreted as fields in this generalized sense, provided a non trivial choice of the renormalization constants is given. A careful analysis shows that the transformation law of Wick powers is characterized by a weight, and it turns out that the sum of fields with different weights breaks the conformal covariance. At this point there is a difference between the previously given picture due to the presence of a bigger group of covariance. It is furthermore shown that the construction does not depend upon the scale mu appearing in the Hadamard parametrix, used to regularize the fields. Finally, we briefly discuss some further examples of more involved fields.
dc.description21 pages, comments added, to appear on Commun. Math. Phys
dc.identifierhttps://arxiv.org/abs/0806.0803
dc.identifierhttp://arxiv.org/abs/0806.0803
dc.identifierCommun.Math.Phys.288:1117-1135,2009
dc.identifierdoi:10.1007/s00220-009-0780-x
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229842
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.titleConformal generally covariant quantum field theory: The scalar field and its Wick products
dc.typetext

Files

Collections

arXiv