2023/12/16 by Benjamín Álvarez, Alvarez, Benjamin, Jacob Schach Møller +1 · 2 citations
Physics and Astronomy · Mathematics · #Quantum Chromodynamics and Particle Interactions #Cold Atom Physics and Bose-Einstein Condensates #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2312.10496
We consider a class of toy models describing a fermion field coupled with a boson field. The model can be viewed as a Yukawa model but with scalar fermions. As in our first paper, the interaction kernels are assumed bounded in the fermionic momentum variable and decaying like |q|-p for large boson momenta q. With no restrictions on the coupling strength, we prove norm resolvent convergence to an ultraviolet renormalized Hamiltonian, when the ultraviolet cutoff is removed. We do this by subtracting a sufficiently large, but finite, number of recursively defined self-energy counter-terms, which may be interpreted as arising from a perturbation expansion of the ground state energy. The renormalization procedure requires a spatial cutoff and works in three dimensions provided p>\frac12, which is as close as one may expect to the physically natural exponent p = \frac12.