Dominic Lewis: Bandlimitation, wavelets and scaled QFT - RQI Circuit Sydney 2023

Please note that the microphone used for this talk was defective.
Title: Shannon 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. For example; an ultraviolet cut-off to quantum field theory provides a natural minimum length scale and gives an isomorphism between continuous and discrete representations of a quantum field through Shannon's sampling theorem. A QFT discretised in such a way will still possess the translational symmetries and conserved Noether charges generally associated with fundamentally continuous systems. We extend on this notion by showing that non-bandlimited quantum field theories can be decomposed into bandlimited ones using Shannon wavelets. Each scale of the wavelet decomposition gives a field theory possessing an ultraviolet 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). We show that for non-interacting quantum fields (and certain engineered interacting ones) the physics of the field at one scale is entirely isolated from that of other scales, meaning that no events at one scale can have any effect on the field at any other scale. For fields that can self-interact we find that despite non-zero couplings between the scales of the field, quantities such as the Feynman propagator between scales remain zero.
Talk delivered in Macquarie University on the 1st of December 2023.

[@frun]

Nonbandlimited qft isomorphism is reminiscent of holography. I think, scale decomposition can be made local with a dispersion, that is dependent on scale.