Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Electrodynamics (QED) Renormalization is a Logical Paradox, Zeta
  Function Regularization is Logically Invalid, and Both are Mathematically
  Invalid   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".

21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph