Abstract
We introduce a new hierarchical modeling of scalar field theories that is based on a set of continuous, piecewise-linear wavelets with Sobolev-orthogonality properties. The set is not a basis, but the difference between the hierarchical models and the realistic models arises entirely from this lack of completeness. Not only is this in elegant contrast to the more familiar hierarchical approximations, but it also raises the possibility of calculating the critical exponent ŋ (which is automatically zero for the familiar hierarchical models).
We call these expansion functions Osiris wavelets and in this chapter we introduce them in two dimensions. Sobolev orthogonality breaks down only between adjacent length scales for these wavelets, and we derive a positive lower bound on the overlap matrix. In the case of the dipole gas we also derive the hierarchical reduction of the renormalization group transformation for this wavelet modeling.
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Battle, G. (2001). Osiris Wavelets and the Dipole Gas. In: Debnath, L. (eds) Wavelet Transforms and Time-Frequency Signal Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0137-3_4
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DOI: https://doi.org/10.1007/978-1-4612-0137-3_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6629-7
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