2009/01/19 by Sergio Albeverio, S. Albeverio, Albeverio, S. +3 · 1 citation
Computer Science · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques #hep-th
paper · pdf · doi:10.48550/arxiv.0901.2806
4 pages, LaTeX
openalex publication_date 2009/01/19 · arxiv created 2010/06/28 · arxiv updated 2010/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Wavelet transform has been attracting attention as a tool for regularization of gauge theories since the first paper of (Federbush, Progr. Theor. Phys. 94, 1135, 1995), where the integral representation of the fields by means of the wavelet transform was suggested: Aμ(x) = (1)/(Cψ) ∫\R+ ×\Rd (1)/(ad) g ((x-b)/(a) ) Aμa(b) (daddb)/(a), with Aμa(b) being understood as the fields Aμ measured at point b∈ \Rd with resolution a∈\R+. In present paper we consider a wavelet-based theory of gauge fields, provide a counterpart of the gauge transform for the scale-dependent fields: Aμa(x)→ Aμa(x)+\dμfa(x), and derive the Ward-Takahashi identities for them.