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).

HEP - theorymathematical physicsquantum physics

Audience: advanced learners

( paper | video )

Comments: Linked paper only covers the first (bandlimitation) part of the talk and not wavelets, which will be included in a future paper.

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Tricontinental Quantum Fundamentals Seminar

Series comments: The Tricontinental Quantum Fundamentals Seminar (3C-QFS) is an online seminar series connecting researchers from Australia, Europe, and America. Our goal is to facilitate discussion between the three continents and bring together those working on foundational topics in relativistic quantum physics, covering but not limited to:

• Measurement, localisation, and causality in relativistic quantum theory
• Energy conditions and quantum inequalities
• Non-locality and observer-dependence of entanglement
• Quantum reference frames and symmetries in quantum theory
• Holography, AdS/CFT, and analogue gravity

For 3C-QFS, we wish to foster an inclusive community and promote open discussion by encouraging a casual atmosphere during the seminars.

The seminars are held online via Zoom, consisting of 40-60 minute talks followed by additional time for questions. We meet every three weeks on Tuesday, alternating between two times in order to connect research communities across two of the three continents.

For those unable to join the seminars live, talks are recorded and hosted on the 3C-QFS YouTube channel.

The seminar series is primarily for students and academics active in the foundations of physics. To sign up for the mailing list and join the seminars live, please complete the registration form on the 3C-QFS website.

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