>>118 補足

t Hooft
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dimensional regularization （次元くりこみ）
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Bernstein–Sato polynomial
（Masaki Kashiwara (2003) give more advanced accounts）
とリンクが繋がるのが面白い

数学者が先回りして
Bernstein–Sato polynomialを物理学のために
用意していたってことですね ；ｐ）

(参考)
https://en.wikipedia.org/wiki/Gerard_%27t_Hooft
Gerardus (Gerard) 't Hooft
The world took little notice, but Veltman was excited because he saw that the problem he had been working on was solved. A period of intense collaboration followed in which they developed the technique of dimensional regularization.

https://en.wikipedia.org/wiki/Dimensional_regularization
Dimensional regularization
Dimensional regularization writes a Feynman integral as an integral depending on the spacetime dimension d and the squared distances (xi−xj)2 of the spacetime points xi, ... appearing in it. In Euclidean space, the integral often converges for −Re(d) sufficiently large, and can be analytically continued from this region to a meromorphic function defined for all complex d. In general, there will be a pole at the physical value (usually 4) of d, which needs to be canceled by renormalization to obtain physical quantities. Etingof (1999) showed that dimensional regularization is mathematically well defined, at least in the case of massive Euclidean fields, by using the Bernstein–Sato polynomial to carry out the analytic continuation.

https://en.wikipedia.org/wiki/Bernstein%E2%80%93Sato_polynomial
In mathematics, the Bernstein–Sato polynomial is a polynomial related to differential operators, introduced independently by Joseph Bernstein (1971) and Mikio Sato and Takuro Shintani (1972, 1974), Sato (1990). It is also known as the b-function, the b-polynomial, and the Bernstein polynomial, though it is not related to the Bernstein polynomials used in approximation theory. It has applications to singularity theory, monodromy theory, and quantum field theory.
Severino Coutinho (1995) gives an elementary introduction, while Armand Borel (1987) and Masaki Kashiwara (2003) give more advanced accounts.