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arXiv 2002.074532020-02-18math.COhep-thmath-phmath.MP

Combinatorial quantum field theory and the Jacobian conjecture

Adrian Tanasa

备注：: 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

英文摘要：

In this short review we first recall combinatorial or ($0-$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.

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