Dominic G. Lewis - Bandlimitation, wavelets, and scaled QFT

Abstract: The likely presence of a fundamental minimum length scale to the universe (motivated by generalised uncertainty principles and UV divergences in quantum field theory to name a few) has led to the application of information theoretic techniques such as bandlimitation to quantum field theory, allowing for field theories to be represented as simultaneously continuous and discrete through Shannon theory.
We extend on this notion by showing that non-bandlimited quantum field theories can be decomposed into bandlimited ones, called scales, using Shannon wavelets. Each scale of the wavelet decomposition gives a field theory possessing an ultraviolet cut-off (and infrared cut-off) and, as a result, an equivalent discrete theory. As such, one can use wavelets to decompose an N+1 dimensional continuous field theory into a 2N+1 dimensional discrete theory (where the scale of the wavelet decomposition is treated as a spatial dimension).
Talk page: researchsemina...
Paper: journals.aps.o...
Linked paper only covers the first (bandlimitation) part of the talk and not wavelets, which will be included in a future paper.
3C-QFS, 16 May 2023