Scaling Algebras and Pointlike Fields: A nonpertubative approach to renormalization

TY - JOUR

T1 - Scaling Algebras and Pointlike Fields

T2 - A nonpertubative approach to renormalization

AU - Bostelmann, Henning

AU - D'Antoni, Claudio

AU - Morsella, Gerardo

PY - 2009/1

Y1 - 2009/1

N2 - We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a naturally defined scaling limit in the sense of Buchholz and Verch; we investigate the effect of this limit on the pointlike fields. Both for the fields and their operator product expansions, a well-defined limit procedure can be established. This can always be interpreted in the usual sense of multiplicative renormalization, where the renormalization factors are determined by our analysis. We also consider the limits of symmetry actions. In particular, for suitable limit states, the group of scaling transformations induces a dilation symmetry in the limit theory.

AB - We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a naturally defined scaling limit in the sense of Buchholz and Verch; we investigate the effect of this limit on the pointlike fields. Both for the fields and their operator product expansions, a well-defined limit procedure can be established. This can always be interpreted in the usual sense of multiplicative renormalization, where the renormalization factors are determined by our analysis. We also consider the limits of symmetry actions. In particular, for suitable limit states, the group of scaling transformations induces a dilation symmetry in the limit theory.

UR - http://www.scopus.com/inward/record.url?scp=56349135405&partnerID=8YFLogxK

U2 - 10.1007/s00220-008-0613-3

DO - 10.1007/s00220-008-0613-3

M3 - Article

SN - 0010-3616

VL - 285

SP - 763

EP - 798

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -