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arXiv · 2211.00351

Absence of submultiplicative norms for Wick-ordered Operator Products

Jakob Geisler
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Abstract

In this paper, a key problem of the rigorous formulation of the renormalization group as a continuous flow is identified. Some essential features of the operator-theoretic renormalization group are recalled, and a family of norms associated to different Banach spaces of Hamiltonians is introduced. From this, three different properties, which should be satisfied by an adequate norm, are derived, e.g., a submultiplicativity with respect to Wick-ordering. A proof is given that none of the norms introduced in this paper satisfy all of these conditions.

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Jakob Geisler. 2022-11-01. Absence of submultiplicative norms for Wick-ordered Operator Products. https://doi.org/10.1063/5.0129895

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