On dilation symmetries arising from scaling limits

Henning Bostelmann, Claudio D'Antoni, Gerardo Morsella

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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.
Original languageEnglish
Pages (from-to)21-60
Number of pages40
JournalCommunications in Mathematical Physics
Issue number1
Publication statusPublished - Feb 2010

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