Investigación

 

Atomic radiative corrections without QED: role of the zero-point field

 

A. M. Cetto, L. de la Peña, and A. Valdés-Hernández

 

Instituto de Física, Universidad Nacional Autónoma de México, Apartado postal 20-364, México, DF, 01000, México, e-mail: ana@física.unam.mx,luis@física.unam.mx,andreavh@física.unam.mx.

 

Received 25 January 2013
Accepted 17 May 2013

 

Abstract

We derive the atomic radiative corrections predicted by QED using an alternative approach that offers the advantage of physical clarity and transparency. The element that gives rise to these corrections is the fluctuating zero-point radiation field (ZPF) of average energy per mode, which —in contrast with QED— is taken here as a primordial real entity in permanent interaction with matter and responsible for its quantization. After briefly recalling how quantum mechanics itself emerges as a result of the balance between the ZPF and radiation reaction, the most important higher-order effects of the radiative terms on the atom are studied. The nonrelativistic QED formulas for the lifetimes and the Lamb shift, as well as the corrections to the latter due to external factors that modify the vacuum field, are thus obtained in a self-consistent approach and without the need to resort to second quantization to the present order of approximation.

Keywords: Radiative corrections; atomic lamb shift; atomic lifetimes; zero-point field.

 

PACS: 03.65.Ta; 05.40.-a; 12.20.-m

 

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Acknowledgments

This work was supported by DGAPA-UNAM through project PAPIITIN106412-2. The authors wish to acknowledge useful comments and suggestions from two referees.

 

References

i. In addition, the present calculation serves to correct a factor 1/2 mistakenly introduced in previously published versions of Eq. (12) and the following.

ii. Note that to get a correct (and finite) result, it is essential to leave in the denominator of this formula the term T²ω⁴_mn ≃ T²ω⁴under resonance due to the presence of radiation reaction ([17,27]). This is a natural term in both QED and SED.

iii. Interestingly, however, by virtue of this proportionality, the ratio of spontaneous to induced transition rates is not altered by a modification of the density of modes.

iv. It seems convenient to comment here on another approach, known as Fluctuational Electrodynamics (FE) (see, for example [42,43]), that deals with fluctuating electromagnetic fields to study the emission of thermal radiation and heat transfer problems (generally at a macroscopic level). According to FE, the charges that constitute matter at temperature T produce, due to thermal agitation, a fluctuating electromagnetic field that is solution of the "stochastic Maxwell equations", which include fluctuating current sources. Contact with the thermodynamics is then established by resorting to the fluctuation-dissipation theorem. As in the FE approach, in SED we are dealing with a random field and derive statistical properties of the system, but in the present theory the field is also present at T = 0 (being precisely the zPF) and, contrary to what is done in FE, here we study the effects of this field on matter at a most fundamental level (both in a physical and a conceptual sense): in SED we are concerned with the properties the zPF imprints in atomic level systems in order to develop a fundamental theory of quantum mechanics. Thus, both approaches pursue different aims, though they may share some qualitative features.

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