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arXiv · 2002.07453

Combinatorial quantum field theory and the Jacobian conjecture

Adrian Tanasa
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Abstract

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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Adrian Tanasa. 2020-02-18. Combinatorial quantum field theory and the Jacobian conjecture. https://arxiv.org/abs/2002.07453

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