Abstract
In this chapter we continue the study initiated in the preceding one and pay specific attention to higher-order effects on matter arising from its interaction with the radiation field, in the quantum regime of SED. More explicitly, we reinsert into the basic dynamical equations the zeropoint field and radiation reaction terms that were dropped in the passage to the radia-tionless limit, and use peturbation theory to study detailed energy balance, atomic stability, stimulated and spontaneous transitions, the Lamb shift, etc. In a single phrase, we proceed to the analysis of phenomena that belong to the realm of quantum electrodynamics but can be explained by resorting to the random (non-quantized) vacuum field. The chapter opens with the essentials of SED perturbation theory, which can be formulated in close correspondence with conventional perturbation theory in quantum mechanics.1
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References
Most of the material used for this chapter can be found in Cetto and de la Peña (1991b) and de la Peña and Cetto (1991a, 1992, 1995a).
This closed expression for the solution is probably the one most frequently used within the interaction representation. The interested reader is referred to the literature for the details [see, e.g., Roman 1965, section 4–3; van Kampen 1981, chapters XIII and XIV; Sterman 1993, Appendix A].
An introduction to linear-response theory can be seen, e.g., in Reichl (1980). The two most useful particular forms of excitation F(t) are a periodic force of given frequency (to probe the frequency response), and an infinitely narrow pulse (to probe the transient behaviour of the system).
The theory of the fluctuation-dissipation theorem can be found, e.g., in Reichl (1980), chapter 15. The general relations were introduced in Callen and Welton (1951), although particular instances were known already in the theory of Brownian motion since the early work of Einstein in 1905. Similar results are known in nonrelativistic QED [see, e.g., Milonni 1988 or 1994, section 7.3].
The corresponding quantum calculation can be found in Sakurai (1967).
A positive Lyapunov exponent is a necessary condition for the existence of chaos, because then nearby trajectories separate exponentially with the evolution of the system. The condition is not sufficient, however, because mixing is also needed for chaos to occur [see, e.g., Lichtenberg and Lieberman 1983, section 5.2; Rafiada 1990, chapter 16].
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© 1996 Springer Science+Business Media Dordrecht
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de la Peña, L., Cetto, A.M. (1996). Radiative Corrections in Linear SED. In: The Quantum Dice. Fundamental Theories of Physics, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8723-5_11
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DOI: https://doi.org/10.1007/978-94-015-8723-5_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4646-8
Online ISBN: 978-94-015-8723-5
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