Wavelets in Field Theory

Abstract

We advocate the use of Daubechies wavelets as a basis for treating a variety of problems in quantum field theory. This basis has both natural large volume and short distance cutoffs, has natural partitions of unity, and the basis functions are all related to the fixed point of a linear renormalization group equation.

42 pages, 2 figures, corrected typos

References in corpus (1)

• Block Diagonalization using SRG Flow Equations

Cited by in corpus (22)

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• Entanglement structure of quantum fields through local probes
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• Nearly optimal quantum algorithm for generating the ground state of a free quantum field theory
• Wavelet representation of light-front quantum field theory
• Efficient Quantum Algorithm for All Quantum Wavelet Transforms
• Multiresolution decomposition of quantum field theories using wavelet bases
• Entanglement in quantum field theory via wavelet representations
• Unifying renormalization group and the continuous wavelet transform
• Wavelets and renormalization group in quantum field theory problems
• On quantization in light-cone variables compatible with wavelet transform
• Wavelets in field theory
• Bosonic entanglement renormalization circuits from wavelet theory
• Multi-scale methods in quantum field theory
• Wavelet field decomposition and UV `opaqueness'
• Renormalization in Wavelet basis
• Wavelet regularization of gauge theories
• Hamiltonian Flow Equations in Daubechies Wavelet Basis
• Hamiltonian formulation of the $1+1$-dimensional ${\varphi }^4$ theory in a momentum-space Daubechies wavelet basis
• Quantum Mechanics in Wavelet Basis
• Are there any Landau poles in wavelet-based quantum field theory?
• An efficient Wavelet-Based Hamiltonian Formulation of Quantum Field Theories using Flow-Equations