Extra-Dimensions effects on the fermion-induced quantum energy in the presence of a constant magnetic field

TL;DR

This paper investigates how extra compact dimensions influence the behavior of fermion-induced quantum energy in a strong magnetic field, revealing a transition from logarithmic to power-law growth due to extra dimensions.

Contribution

It provides a detailed analysis of the impact of extra dimensions on quantum energy behavior under strong magnetic fields, extending previous four-dimensional results.

Findings

Quantum energy growth shifts from logarithmic to power-law with extra dimensions.

Strong magnetic fields amplify the effects of extra dimensions on quantum energy.

Results are relevant for theories with compactified extra dimensions.

Abstract

We consider a U(1) gauge field theory with fermion fields (or with scalar fields) that live in a space with $\delta$ extra compact dimensions, and we compute the fermion-induced quantum energy in the presence of a constant magnetic field, which is directed towards the x_3 axis. Our motivation is to study the effect of extra dimensions on the asymptotic behavior of the quantum energy in the strong field limit (eB>>M^{2}), where M=1/R. We see that the weak logarithmic growth of the quantum energy for four dimensions, is modified by a rapid power growth in the case of the extra dimensions.