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Stochastic inflationary scalar electrodynamics. (English) Zbl 1151.81030
The paper deals with the problem of generalizing the A. A. Starobinskiĭ’s stochastic formalism [cf. Stochastic de Sitter (inflationary) stage in the early universe Field Theory, in: Eds. de Vega H.J. and Sanchez N., Quantum Gravity and Strings, Springer, 107–126 (1986)] in order to be able to gain a nonperturbative control over infrared logarithms that may be exhibited by Green’s functions of quantum field models other than that describing self-interacting massless scalars minimally coupled to a de Sitter inflationary background. More precisely, the authors aim at deriving a leading logarithmic solution for a model of massless scalar electrodynamics on a de Sitter space-time. In doing so, they move from results of S.-P. Miao and R. P. Woodard [Leading Log Solution for Inflationary Yukawa, Physical Review, D74,044019 (2006)] (see also [R. P. Woodard, Generalizing Starobinskiĭ’s Formalism to Yukawa Theory and to Scalar QED, Journal of Physics: Conference Series, 68, 012032 (2007)]), where the suggestion has been given to attempt to construct effective stochastic models for fields that really do produce infrared logarithms after properly integrating out fields that actually do not; this strategy has been there shown to work for a model involving a Yukawa coupling between massless scalar field and massless fermion.
For general models a complication stands, however, in the possible presence of derivative interactions, whose general treatment is still to be understood. For the inflationary scalar electrodynamics case under investigation in the present paper, the authors show that these actually play no role at the leading logarithmic order and that one is basically concerned with a scalar field model with an effective potential bounded below. This circumstance enables them to accomplish nonperturbative predictions for their model according to results established in Ref. [A. A. Starobinskiĭ, J. Yokoyama, Equilibrium state of a self-interacting scalar field in the de Sitter background, Physical Review, D50, 6357–6368 (1994)]. In particular, the authors stochastically compute the expectation value of the stress tensor (including the scalar field kinetic and the e.m. strenght bilinears) and confirm the conjecture of Ref. [K. Dimopoulos, T. Prokopec, O. Törnkvist, A. C. Davis, Natural magnetogenesis from inflation, Physical Review, D65, 063505 (2002)] that super-horizon photons acquire mass during inflation.
Similarly to other works by the same authors, the paper is well written and self-consistent. The formalism, the motivations, and the results are detailed and elucidated with care and effectiveness. From the initial discussion of sources of infrared logarithms to concluding arguments concerning possible physical interpretations of results, readers are guided step by step into key aspects of the matter; in case, they can also take advantage of an exhaustive bibliography section. It would not be surprising that even those theoretical and mathematical physicists that are not familiar with topics touched in the manuscript will find its reading interesting and constructive in some respects.

81T20 Quantum field theory on curved space or space-time backgrounds
83F05 Relativistic cosmology
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
83C47 Methods of quantum field theory in general relativity and gravitational theory
81V10 Electromagnetic interaction; quantum electrodynamics
81S20 Stochastic quantization
81T18 Feynman diagrams
Full Text: DOI
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