Causal signal transmission by quantum fields. I: Response of the harmonic oscillator

Abstract

It is shown that response properties of a quantum harmonic oscillator are in essence those of a classical oscillator, and that, paradoxical as it may be, these classical properties underlie all quantum dynamical properties of the system. The results are extended to non-interacting bosonic fields, both neutral and charged.

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

“…An attempt to apply methods of real-time QFT to quantum optics was made by Vinogradov and Stenholm [32]. Generalisation of the conventional time-normal operator ordering [12][13][14] beyond the resonance approximation, making it applicable in relativity, was introduced in [2] for bosons and [3] for fermions.…”

“…Here our goal is the opposite: we wish to apply wisdom acquired in quantum optics to QFT. The result of this paper in a nutshell is that, firstly, the nonequilibrium real-time QFT is nothing but the nonlinear quantum response problem formulated in phase-space terms, and, secondly, that the most natural physical picture emerges if using the phase-space mapping based on the so-called time-normal operator ordering [2,[12][13][14]. Moreover, in relativistic quantum electrodynamics (QED), mappings based on other orderings (e.g., the Keldysh rotation [11,15]) lead to inconsistencies, due to one's well-known inability to impose the Lorentz condition on the operator of the electromagnetic potential.…”

“…In papers [1][2][3], we introduced response transformation of quantum kinematics. In paper [4], response transformation was extended to the key technical tool of quantum field theory (QFT), Wick's theorem [5][6][7][8].…”

“…Moreover, in relativistic quantum electrodynamics (QED), mappings based on other orderings (e.g., the Keldysh rotation [11,15]) lead to inconsistencies, due to one's well-known inability to impose the Lorentz condition on the operator of the electromagnetic potential. Imposing this condition on quantum states of the electromagnetic field [16,17] is not sufficient to cancel unphysical contributions to its fluctuations, except in the time-normally-ordered representation (termed in [1][2][3] …”

“…Papers [1][2][3] were intended predominantly for the quantum-optical community; our goal was in particular to "market" QFT methods to quantum opticians. Here our goal is the opposite: we wish to apply wisdom acquired in quantum optics to QFT.…”