Combinatorial quantum field theory and the Jacobian conjecture
Abstract
In this short review we first recall combinatorial or (dimensional) quantum field theory (QFT). We then give the main idea of a standard QFT method, called the intermediate field method, and we review how to apply this method to a combinatorial QFT reformulation of the celebrated Jacobian conjecture on the invertibility of polynomial systems. This approach establishes a related theorem concerning partial elimination of variables that implies a reduction of the generic case to the quadratic one. Note that this does not imply solving the Jacobian conjecture, because one needs to introduce a supplementary parameter for the dimension of a certain linear subspace where the system holds.
Keywords
Cite
@article{arxiv.2002.07453,
title = {Combinatorial quantum field theory and the Jacobian conjecture},
author = {Adrian Tanasa},
journal= {arXiv preprint arXiv:2002.07453},
year = {2020}
}
Comments
9 pages, 1 figure, invited review paper for the Proceedings of the conference Transient Transcendence in Transylvania, Brasov, May 13 - 17, 2019. This article draws heavily from arXiv:1411.6558