On dilation symmetries arising from scaling limits

TY - JOUR

T1 - On dilation symmetries arising from scaling limits

AU - Bostelmann, Henning

AU - D'Antoni, Claudio

AU - Morsella, Gerardo

PY - 2010/2

Y1 - 2010/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=72249109639&partnerID=8YFLogxK

U2 - 10.1007/s00220-009-0899-9

DO - 10.1007/s00220-009-0899-9

M3 - Article

SN - 0010-3616

VL - 294

SP - 21

EP - 60

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -