Problems with the Newton-Schr\"odinger Equations

We examine the origin of the Newton-Schr\"odinger equations (NSEs) that play an important role in alternative quantum theories (AQT), macroscopic quantum mechanics and gravity-induced decoherence. We show that NSEs for individual particles do not follow from general relativity (GR) plus quantum field theory (QFT). Contrary to what is commonly assumed, the NSEs are not the weak-field (WF), non-relativistic (NR) limit of the semi-classical Einstein equation (SCE) (this nomenclature is preferred over the `M\/oller-Rosenfeld equation') based on GR+QFT. The wave-function in the NSEs makes sense only as that for a mean field describing a system of $N$ particles as $N \rightarrow \infty$, not that of a single or finite many particles. From GR+QFT the gravitational self-interaction leads to mass renormalization, not to a non-linear term in the evolution equations of some AQTs. The WF-NR limit of the gravitational interaction in GR+QFT involves no dynamics. To see the contrast, we give a derivation of the equation (i) governing the many-body wave function from GR+QFT and (ii) for the non-relativistic limit of quantum electrodynamics (QED). They have the same structure, being linear, and very different from NSEs. Adding to this our earlier consideration that for gravitational decoherence the master equations based on GR+QFT lead to decoherence in the energy basis and not in the position basis, despite some AQTs desiring it for the `collapse of the wave function', we conclude that the origins and consequences of NSEs are very different, and should be clearly demarcated from those of the SCE equation, the only legitimate representative of semiclassical gravity, based on GR+QFT.Comment: 18 pages. Invited paper for the Focus Issue on 'Gravitational quantum physics' in New Journal of Physic

N-particle sector of quantum field theory as a quantum open system

We give an exposition of a technique, based on the Zwanzig projection formalism, to construct the evolution equation for the reduced density matrix corresponding to the n-particle sector of a field theory. We consider the case of a scalar field with a $g \phi^3$ interaction as an example and construct the master equation at the lowest non-zero order in perturbation theory.Comment: 12 pages, Late

Continuous-time histories: observables, probabilities, phase space structure and the classical limit

In this paper we elaborate on the structure of the continuous-time histories description of quantum theory, which stems from the consistent histories scheme. In particular, we examine the construction of history Hilbert space, the identification of history observables and the form of the decoherence functional (the object that contains the probability information). It is shown how the latter is equivalent to the closed-time-path (CTP) generating functional. We also study the phase space structure of the theory first through the construction of general representations of the history group (the analogue of the Weyl group) and the implementation of a histories Wigner-Weyl transform. The latter enables us to write quantum theory solely in terms of phase space quantities. These results enable the implementation of an algorithm for identifying the classical (stochastic) limit of a general quantum system.Comment: 46 pages, latex; in this new version typographical errors have been removed and the presentation has been made cleare