Operator-algebraic renormalization and wavelets

Alexander Stottmeister; Gerardo Morsella; Vincenzo Morinelli; Yoh Tanimoto

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Operator-algebraic renormalization and wavelets

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arxiv 2002.01442 v2 pith:FEHRURRN submitted 2020-02-04 math-ph math.MPmath.OAquant-ph

Alexander Stottmeister , Vincenzo Morinelli , Gerardo Morsella , Yoh Tanimoto This is my paper

classification math-phmath.MPmath.OAquant-ph

keywords renormalizationlatticesystemscontinuumfieldgrouplimitoperator-algebraic

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We report on a rigorous operator-algebraic renormalization group scheme and construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets. Causality follows from Lieb-Robinson bounds for harmonic lattice systems. The scheme is related with the multi-scale entanglement renormalization ansatz and augments the semi-continuum limit of quantum systems.

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