论文标题
量子电动力学（QED）重新归一化是逻辑悖论，Zeta函数正则化在逻辑上无效，并且两者在数学上都是无效的
Quantum Electrodynamics (QED) Renormalization is a Logical Paradox, Zeta Function Regularization is Logically Invalid, and Both are Mathematically Invalid
论文作者
论文摘要
量子动力学（QED）肾上腺素化是悖论。它使用Euler-Mascheroni常数，该常数由有条件收敛的系列定义。但是里曼的系列定理证明，任何有条件收敛的系列都可以重新排列以发散。这个矛盾（既收敛又是发散的系列）是“经典”逻辑，直觉逻辑和zermelo-fraenkel集理论中的悖论，并且也与加法的交换性和关联性质相矛盾。因此，QED在数学上是无效的。 Zeta函数正则化等同于它们在域值处的Zeta函数的两个定义（其中DIRICHLET系列的定义是不同的，Riemann的定义是收敛的）。这样做会产生悖论（如果Riemann的定义为真），或者在逻辑上是无效的（如果Riemann的定义是FALSE）。我们证明了里曼的定义是错误的，因为里曼的定义的推导包括矛盾：汉克尔轮廓和库奇的整体定理的使用。同样，事实证明，Zeta函数的第三个定义是错误的。 Zeta函数没有零，因此由于物质的含义和“空虚的受试者”，Riemann假设是悖论。
Quantum Electrodynamics (QED) renormalizaion is a paradox. It uses the Euler-Mascheroni constant, which is defined by a conditionally convergent series. But Riemann's series theorem proves that any conditionally convergent series can be rearranged to be divergent. This contradiction (a series that is both convergent and divergent) is a paradox in "classical" logic, intuitionistic logic, and Zermelo-Fraenkel set theory, and also contradicts the commutative and associative properties of addition. Therefore QED is mathematically invalid. Zeta function regularization equates two definitions of the Zeta function at domain values where they contradict (where the Dirichlet series definition is divergent and Riemann's definition is convergent). Doing so either creates a paradox (if Riemann's definition is true), or is logically invalid (if Riemann's definition is false). We show that Riemann's definition is false, because the derivation of Riemann's definition includes a contradiction: the use of both the Hankel contour and Cauchy's integral theorem. Also, a third definition of the Zeta function is proven to be false. The Zeta function has no zeros, so the Riemann hypothesis is a paradox, due to material implication and "vacuous subjects".
