arXiv subjects

Gerardo Morsella

Publications and source records attributed to Gerardo Morsella.

23 records · Page 2Linked to original sources

arXiv2008

Scaling algebras and pointlike fields: A nonperturbative approach to renormalization

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.

math-ph↗

arXiv2008

Scaling limit for subsystems and Doplicher-Roberts reconstruction

Given an inclusion $B \subset F$ of (graded) local nets, we analyse the structure of the corresponding inclusion of scaling limit nets $B_0 \subset F_0$, giving conditions, fulfilled in free field theory, under which the unicity of the scaling limit of $F$ implies that of the scaling limit of $B$. As a byproduct, we compute explicitly the (unique) scaling limit of the fixpoint nets of scalar free field theories. In the particular case of an inclusion $A \subset B$ of local nets with the same canonical field net $F$, we find sufficient conditions which entail the equality of the canonical field nets of $A_0$ and $B_0$.

math.OA↗

arXiv2006

Scaling Algebras and Superselection Sectors: Study of a Class of Models

We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R. Verch). In particular, we show that for each pair (G, N), with G a compact Lie group and N a closed normal subgroup, there is a net of observable algebras which has (a subset of) DHR sectors in 1-1 correspondence with classes of irreducible representations of G, and such that only the sectors corresponding to representations of G/N are preserved in the scaling limit. In the way of achieving this result, we derive sufficient conditions under which the scaling limit of a tensor product theory coincides with the product of the scaling limit theories.

math-ph↗

arXiv2003

Scaling algebras for charged fields and short-distance analysis for localizable and topological charges

The method of scaling algebras, which has been introduced earlier as a means for analyzing the short-distance behaviour of quantum field theories in the setting of the model-independent, operator-algebraic approach, is extended to the case of fields carrying superselection charges. In doing so, consideration will be given to strictly localizable charges ("DHR-type" superselection charges) as well as to charges which can only be localized in regions extending to spacelike infinity ("BF-type" superselection charges). A criterion for the preservance of superselection charges in the short-distance scaling limit is proposed. Consequences of this preservance of superselection charges are studied. The conjugate charge of a preserved charge is also preserved, and for charges of DHR-type, the preservance of all charges of a quantum field theory in the scaling limit leads to equivalence of local and global intertwiners between superselection sectors.

math-ph↗

arXiv2002

The Structure of Charges in the Ultraviolet and an Intrinsic Notion of Confinement

After a brief account of the algebraic version of renormalization group developed by Buchholz and Verch, and of the main results of the Doplicher-Haag- Roberts theory of superselection sectors, we introduce the notion of asymptotic charge transfer chain, through which it is possible to reconstruct the scaling limit theory's superselection structure entirely in terms of underlying theory's observables. Furthermore, these objects allow the formulation of a natural notion of preservation of a charge in the scaling limit, so that one gets an intrinsic definition of confined charges, as those charges of the scaling limit which do not come from preserved charges of the underlying theory. This is an expository account of the results. Proofs will be published elsewhere.

math-ph↗