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On dilation symmetries arising from scaling limits

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Publication details

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


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.


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