4 research outputs found
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.Comment: minor changes and clarifications; as to appear in Commun. Math.
Phys.; 37 page
On dilation symmetries arising from scaling limits
Quantum field theories, at short scales, can be approximated by a scaling
limit theory. In this approximation, an additional symmetry is gained, namely
dilation covariance. To understand the structure of this dilation symmetry, we
investigate it in a nonperturbative, model independent context. To that end, it
turns out to be necessary to consider non-pure vacuum states in the limit.
These can be decomposed into an integral of pure states; we investigate how the
symmetries and observables of the theory behave under this decomposition. In
particular, we consider several natural conditions of increasing strength that
yield restrictions on the decomposed dilation symmetry.Comment: 40 pages, 1 figur