Causal signal transmission by quantum fields. V: Generalised Keldysh rotations and electromagnetic response of the Dirac sea

Abstract

The connection between real-time quantum field theory (RTQFT) [see, e.g., A. Kamenev and A. Levchenko, Advances in Physics 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 [Phys. Rev. 177 (1969) 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 electromagnetic field 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 electromagnetic field under orderings other than time-normal. The resulting expression is physically inconsistent: it does not obey the Lorentz condition, nor Maxwell's equations.

Modelling of weak quantum measurements consistent with conservation laws

“…In the lowest order we can also neglect allK q aq . In the g → 0 limit n-correlation of the sequence of measurementsÂ,B,Ĉ, reads [16,17]…”

The linear optical response of the quantum vacuum

“…(22) In this form gauge invariance is obvious but note that both terms were required to give this result [16].…”

Quantum theory of an electromagnetic observer: Classically behaving macroscopic systems and the emergence of the classical world in quantum electrodynamics

“…The whole procedure is highly nontrivial because of divergences and renormalisations. For details, see textbooks [5][6][7] and papers [9,10].…”

“…Paradoxical as it may sound, it is also the "strict causality" that makes it unphysical, because it implies one's ability to vary sorces arbitrarily on microscopic scales. Application of the responce formulation to a solitary electromagnetic device [9,10] and its extention to electromagnetic interactions of distinguishable devices (Sec. VII of this paper) preserve both its advantages (causality and intuitiveness) and its main drawback (unphysical nature of c-number souces).…”