Some improved nonperturbative bounds for Fermionic expansions

TL;DR

This paper introduces improved nonperturbative bounds for Fermionic expansions by utilizing a recursive approach, offering advantages over traditional Fourier-based bounds, especially for models like the cold interacting Fermi gas.

Contribution

It presents a novel recursive method for bounding Fermionic expansion amplitudes, providing tighter bounds without relying on Fourier transforms.

Findings

New bounds for Fermionic amplitudes that avoid Fourier transform

Enhanced convergence estimates for Fermionic perturbative expansions

Applicable to models like the cold interacting Fermi gas

Abstract

We reconsider the Gram-Hadamard bound as it is used in constructive quantum field theory and many body physics to prove convergence of Fermionic perturbative expansions. Our approach uses a recursion for the amplitudes of the expansion, discovered originally by Djokic arXiv:1312.1185. It explains the standard way to bound the expansion from a new point of view, and for some of the amplitudes provides new bounds, which avoid the use of Fourier transform, and are therefore superior to the standard bounds for models like the cold interacting Fermi gas.