Violation of the Lorentz symmetry has important effects on physical quantities including field propagators. Therefore, in addition to the leading order, the sub-leading order of quantities may be modified. In this paper, we calculate the next to leading (NLO) radiative corrections to the Casimir energy in the presence of two perfectly conducting parallel plates for φ 4 theory with a Lorentz-breaking extension. We do the renormalization and investigate these NLO corrections for three distinct directions of the Lorentz violation; temporal direction, parallel and perpendicular to the plates.

In this paper, we investigate one-loop radiative corrections to the Casimir energy in the presence of two perfectly conducting parallel plates for QED theory within the renormalized perturbation theory. In fact, there are three contributions for radiative corrections to the Casimir energy, up to order α. Only the two-loop diagram, which is of order α, has been computed by Bordag et. al (1985), approximately. Here, up to this order, we consider corrections due to two one-loop terms, i.e., photonic and fermionic loop corrections resulting from renormalized QED Lagrangian, more precisely. Our results show that only the fermionic loop has a very minor correction and the correction of photonic loop vanishes.

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Mass renormalization of the electron in configurations such as metallic hydride surfaces due to electromagnetic field fluctuations leads to mass enhancement of the electron, which is known as the heavy electron. The effective mass renormalization has substantial consequences in the theory of electromagnetic field interaction with matter (QED). One of the fascinating effects appears when an external photon interacts with the heavy electron. In this case, the wavelength of the scattered photon from the electron increases and the hard photon turns into a soft photon. In this paper, we present a novel mechanism to show how the heavy electron results in hard photon absorption.

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