Wavelet methods in quantum field theory

Wayne Polyzou, PhD

This is a talk that I will present (by zoom) at JLAB later this month.
I will discuss a representation of local quantum fields using Daubechies' wavelets, which are fractal-valued functions that are useful for data compression (related functions are used in jpeg photographs, the film industry, and the FBI fingerprint database). Basis functions are generated from the fixed point of a renormalization group equation by scale transformations and translations. While the basis functions are fractal valued, they can locally pointwise represent low-degree polynomials. They are used to give an exact representation of local fields as an expansion in well-defined, discrete almost local field operators satisfying canonical commutation relations. Singular operator products are replaced by infinite sums of well-defined products of operators. While the sums are generally ill defined, natural resolution and volume truncations replace the infinite sums by finite sums. Truncations at different resolutions are exactly related by a renormalization of the coefficients in the Hamiltonian and a canonical transformation. I will show how flow equation methods can be used to integrate out short distance degrees of freedom (T. Michlin) and I will also discuss an application evaluating a real-time path integrals treated as the expectation value a complex probability on a space of cylinder sets of discrete paths ( a method due to Palle and E. Nathanson).

To participate in this event via Zoom, go to https://uiowa.zoom.us/j/99570315915.