English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A comprehensive analysis on the photon self-energy, the fermion self-energy,and the fermion vertex function is presented at one loop in the context ofquantum electrodynamics (QED) with 1 extra dimension. In 5-dimensionaltheories, characterized by an infinite number of Kaluza-Klein fields, one-loopamplitudes involve discrete as well as continuous sums, $\sum^\infty_{n=1}\intd^4k$, that could diverge. Using dimensional regularization, we express suchsums as products of gamma and Epstein functions, both defined on the complexplane, with divergences arising from poles of these functions in the limit as $D \to 4$. Using the analytical properties of the Epstein function, we show thatthe ultraviolet divergences generated by the Kaluza-Klein sums can beconsistently renormalized, which means that the corresponding renormalizedquantities reduce to the usual ones of QED at the limit of a very largecompactification scale $R^{-1}$. The main features of QED at the one-loop levelwere studied. We use the mass-dependent $\mu$-scheme to calculate, in QED withan arbitrary number $n$ of extra dimensions, a beta function fulfilling alldesirable physical requirements. We argue that in this type of theories, with alarge mass spectrum covering a wide energy range, beta functions should not becalculated by using mass-independent renormalization schemes. We show that thebeta function is finite for any energy $\mu$. In particular, it reduces to theusual QED result $e^3/12\pi^2$ for $m\ll \mu \ll R^{-1}$ and vanishes for $m\gg\mu$, with $m$ the usual fermion mass. Throughout the work, the decouplingnature of all our results obtained from the analytical properties of theEpstein function is stressed.

Implications of extra dimensions on the effective charge and the beta function in quantum electrodynamics