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Causal signal transmission by quantum fields. V: Generalised Keldysh rotations and electromagnetic response of the Dirac sea
KTH, School of Engineering Sciences (SCI), Physics. (Kvantoptik)
2012 (English)In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 327, no 11, 2691-2741 p.Article in journal (Refereed) Published
Abstract [en]

The connection between real-time quantum field theory (RTQFT) [see, e.g., A.Kamenev and A.Levchenko, Adv. Phys. 58 (2009) 197] and phase-space techniques [E.Wolf and L.Mandel, Optical Coherence and Quantum Optics (Cambridge, 1995)] is investigated. The Keldysh rotation that forms the basis of RTQFT is shown to be a phase-space mapping of the quantum system based on the symmetric (Weyl) ordering. Following this observation, we define generalised Keldysh rotations based on the class of operator orderings introduced by Cahill and Glauber [K.E. Cahill, R.J. Glauber, Phys.Rev.177 (1969) 1882]. Each rotation is a phase-space mapping, generalising the corresponding ordering from free to interacting fields. In particular, response transformation [L.I.Plimak, S.Stenholm, Ann.Phys. (N.Y.) 323 (2008) 1989] extends the normal ordering of free-field operators to the time-normal ordering of Heisenbergoperators. Structural properties of the response transformation, such as its association with the nonlinear quantum response problem and the related causality properties, hold for all generalised Keldysh rotations.Furthermore, we argue that response transformation is especially suited for RTQFT formulation of spatial, in particular, relativistic, problems, because it extends cancellation of zero-point fluctuations, characteristic of the normal ordering, to interacting fields. As an example, we consider quantised electromagneticfield in the Dirac sea. In the time-normally-ordered representation, dynamics of the field looks essentially classical (fields radiated by currents), without any contribution from zero-point fluctuations. For comparison, we calculate zero-point fluctuations of the interacting electromagneticfield under orderings other than time-normal. The resulting expression is physically inconsistent: it does not obey the Lorentz condition, nor Maxwell's equations.

Place, publisher, year, edition, pages
2012. Vol. 327, no 11, 2691-2741 p.
Keyword [en]
Phase-space methods, Quantum field theory, Quantum-statistical response problem
National Category
Physical Sciences
URN: urn:nbn:se:kth:diva-103513DOI: 10.1016/j.aop.2012.06.007ISI: 000308687500005ScopusID: 2-s2.0-84865420112OAI: diva2:561051

QC 20121017

Available from: 2012-10-17 Created: 2012-10-15 Last updated: 2012-10-29Bibliographically approved

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