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To unify the quantum electrodynamics (QED) under the first principle which brings the renormalization unartificially, we study Feynman diagrams in QED according to the set theory and the category theory. We add the restriction on the electromagnetic interaction that a particle can and only can interact with particles which never interact with onself. Thus, fermiors (lines) in tree diagrams belong to sets, but belong to proper classes when they are in five primitive divergent diagrams. Fermiors, photons, fermior mass and charge compose together categories in which the group product of the local U(1) group and the propr Lorentz group is the morphism. There is the functor projecting the category containing fermiors in tree diagrams into the category containing fermior in divergent diagrams. Because proper classes have not the measure, this functor avoids the restriction of the measure. It can be regarded as the renormalization in QED and all renormalization constants have not a fixed magnitude.
In this paper we present background results in enriched category theory and enriched model category theory necessary for developing model categories of enriched functors suitable for doing functor calculus.
Adjoint functor theorems give necessary and sufficient conditions for a functor to admit an adjoint. In this paper we prove general adjoint functor theorems for functors between $infty$-categories. One of our main results is an $infty$-categorical ge
Orlovs famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. In this paper we show that this result is false without the full faithfulness hypothesis.
We develop a theory of Frobenius functors for symmetric tensor categories (STC) $mathcal{C}$ over a field $bf k$ of characteristic $p$, and give its applications to classification of such categories. Namely, we define a twisted-linear symmetric monoi
We compute the on-shell wave function renormalization constant to four-loop order in QCD and present numerical results for all coefficients of the SU$(N_c)$ colour factors. We extract the four-loop HQET anomalous dimension of the heavy quark field an