5,208 research outputs found

### 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

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