几位作者用海森伯图象指出，原子跃迁、基态稳定性和位置-动量对易关系[x，p]=ih，只能通过引入辐射反应和真空电磁涨落力来解释。在这里，我们考虑一个简单的情况下，非相对论带电谐振子，在一维，研究如何考虑辐射反应和真空涨落力的薛定谔图片。我们考虑了经典零点和热电磁真空场的影响。我们表明，零点的电磁涨落的动力学有关的动量算符p=-ihd/dx中使用的薛定谔图片。因此，在薛定谔方程中使用的矢势A_x（t）中引入零点电磁场产生"双重计数“，如A. J. Faria等人最近所示（Physics Letters A 305（2002）322）。本文详细地说明了如何在薛定谔方程中只引入辐射反应和热电磁场来避免"双重计数“。
英文摘要：
Several authors have used the Heisenberg picture to show that the atomic transitions, the stability of the ground state and the position-momentum commutation relation [x,p]=ih, can only be explained by introducing radiation reaction and vacuum electromagnetic fluctuation forces. Here we consider the simple case of a nonrelativistic charged harmonic oscillator, in one dimension, to investigate how to take into account the radiation reaction and vacuum fluctuation forces within the Schrodinger picture. We consider the effects of both classical zero-point and thermal electromagnetic vacuum fields. We show that the zero-point electromagnetic fluctuations are dynamically related to the momentum operator p=-ih d/dx used in the Schrodinger picture. Consequently, the introduction of the zero-point electromagnetic fields in the vector potential A_x(t) used in the Schrodinger equation, generates ``double counting'', as was shown recently by A.J. Faria et al. (Physics Letters A 305 (2002) 322). We explain, in details, how to avoid the ``double counting'' by introducing only the radiation reaction and the thermal electromagnetic fields into the Schrodinger equation.
The Janszky representation constructs quantum states of a field mode as a superposition of coherent states on a line in the complex plane. We show that this provides a natural Schrödinger picture description of the interference between a pair of modes at a beam splitter.
The Schrodinger and Heisenberg pictures are equivalent formulations of quantum mechanics. Here we use the Schrodinger picture to calculate the decoherence that occurs when an optical Schrodinger cat state is passed through a beam splitter. We find that an exponentially large amount of decoherence can occur even when there is a negligible change in the quadrature operator x(t) in the Heisenberg picture. Similar results have been observed in the decoherence produced by an optical amplifier, and we suggest that the usual quadrature operators in the Heisenberg picture do not provide a complete des…
The effects of the entanglement of the inflaton field which initially entangled with those of another field on observables like power spectrum are known in the context of the Schrödinger field theory. To clarify this effect in Heisenberg picture, there were some attempts to construct the initial entangled state by making use of an entangled transformation (like Bogoliubov transformation) between the Bunch-Davies vacuums and squeezed states. We study the role of the time-dependent entangled transformation in the Schrödinger field theory. We derive the relation between two vacuum states which th…
We study all-optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum, using the collision of two focused high-intensity laser pulses as an example. The experimental signatures of quantum vacuum nonlinearities are encoded in signal photons, whose kinematic and polarization properties differ from the photons constituting the macroscopic laser fields. We implement an efficient numerical algorithm allowing for the theoretical investigation of such signatures in realistic field configurations accessible in experiment. This algorithm is based on a v…
Optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum can be conveniently described in terms of stimulated photon emission processes induced by strong classical, space-time dependent electromagnetic fields. Recent studies have adopted this approach to study collisions of Gaussian laser pulses in paraxial approximation. The present study extends these investigations beyond the paraxial approximation by using an efficient numerical solver for the classical input fields. This new numerical code allows for a consistent theoretical description of…
一些众所周知的影响，关于真空下的形式主义的时间场论重新审视。根据这些效应，它们可能意味着在不同的情况下存在一个热真空。真空的瞬时哈密顿量不仅能为Casimir效应和Van der Waals力的计算提供精确的分布函数，而且还能提供截止函数。温鲁效应的热浴是由时间格林函数构造的。从弯曲时空的场论出发，根据不同的真空态定义了场量子化，并导出了霍金辐射，引入的共形不变性与弯曲时空场论的形式一致.弯曲时空中的感生格林函数与热真空中的感生格林函数是一致的。
