5,388 research outputs found
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 interaction as an example and construct the
master equation at the lowest non-zero order in perturbation theory.Comment: 12 pages, Late
Non-Equilibrium Quantum Electrodynamics
We employ the influence functional technique to trace out the photonic
contribution from full quantum electrodynamics. The reduced density matrix
propagator for the spinor field is then constructed. We discuss the role of
time-dependent renormalization in the propagator and focus on the possibility
of obtaining dynamically induced superselection rules. Finally, we derive the
master equation for the case of the field being in an one-particle state in a
non-relativistic regime and discuss whether EM vacuumm fluctuations are
sufficient to produce decoherence in the position basis.Comment: 28 pages, 2 figures. Substantially revised, one important mistake
corrected; discussion on decoherence upgraded, section 4 essentially
rewritte
Information measures and classicality in quantum mechanics
We study information measures in quantu mechanics, with particular emphasis
on providing a quantification of the notions of classicality and
predictability. Our primary tool is the Shannon - Wehrl entropy I. We give a
precise criterion for phase space classicality and argue that in view of this
a) I provides a measure of the degree of deviation from classicality for closed
system b) I - S (S the von Neumann entropy) plays the same role in open systems
We examine particular examples in non-relativistic quantum mechanics. Finally,
(this being one of our main motivations) we comment on field classicalisation
on early universe cosmology.Comment: 35 pages, LATE
Quantum Fields in Nonstatic background: A Histories Perspective
For a quantum field living on a non - static spacetime no instantaneous
Hamiltonian is definable, for this generically necessitates a choice of
inequivalent representation of the canonical commutation relations at each
instant of time. This fact suggests a description in terms of time - dependent
Hilbert spaces, a concept that fits naturally in a (consistent) histories
framework. Our primary tool for the construction of the quantum theory in a
continuous -time histories format is the recently developed formalism based on
the notion of the history group . This we employ to study a model system
involving a 1+1 scalar field in a cavity with moving boundaries.
The instantaneous (smeared) Hamiltonian and a decoherence functional are then
rigorously defined so that finite values for the time - averaged particle
creation rate are obtainable through the study of energy histories. We also
construct the Schwinger - Keldysh closed- time - path generating functional as
a ``Fourier transform'' of the decoherence functional and evaluate the
corresponding n - point functions.Comment: 27 pages, LATEX; minor changes and corrections; version to appear in
JM
Characterizing Multiple Solutions to the Time-Energy Canonical Commutation Relation via Quantum Dynamics
We address the multiplicity of solutions to the time-energy canonical
commutation relation for a given Hamiltonian. Specifically, we consider a
particle spatially confined in a potential free interval, where it is known
that two distinct self-adjoint and compact time operators conjugate to the
system Hamiltonian exist. The dynamics of the eigenvectors of these operators
indicate that different time operators posses distinguishing properties that
can unambiguously associate them to specific aspects of the quantum time
problem
Classical Vs Quantum Probability in Sequential Measurements
We demonstrate in this paper that the probabilities for sequential
measurements have features very different from those of single-time
measurements. First, they cannot be modelled by a classical stochastic process.
Second, they are contextual, namely they depend strongly on the specific
measurement scheme through which they are determined. We construct
Positive-Operator-Valued measures (POVM) that provide such probabilities. For
observables with continuous spectrum, the constructed POVMs depend strongly on
the resolution of the measurement device, a conclusion that persists even if we
consider a quantum mechanical measurement device or the presence of an
environment. We then examine the same issues in alternative interpretations of
quantum theory. We first show that multi-time probabilities cannot be naturally
defined in terms of a frequency operator. We next prove that local hidden
variable theories cannot reproduce the predictions of quantum theory for
sequential measurements, even when the degrees of freedom of the measuring
apparatus are taken into account. Bohmian mechanics, however, does not fall in
this category. We finally examine an alternative proposal that sequential
measurements can be modelled by a process that does not satisfy the Kolmogorov
axioms of probability. This removes contextuality without introducing
non-locality, but implies that the empirical probabilities cannot be always
defined (the event frequencies do not converge). We argue that the predictions
of this hypothesis are not ruled out by existing experimental results
(examining in particular the "which way" experiments); they are, however,
distinguishable in principle.Comment: 56 pages, latex; revised and restructured. Version to appear in
Found. Phy
Coarse Grainings and Irreversibility in Quantum Field Theory
In this paper we are interested in the studying coarse-graining in field
theories using the language of quantum open systems. Motivated by the ideas of
Calzetta and Hu on correlation histories we employ the Zwanzig projection
technique to obtain evolution equations for relevant observables in
self-interacting scalar field theories. Our coarse-graining operation consists
in concentrating solely on the evolution of the correlation functions of degree
less than , a treatment which corresponds to the familiar from statistical
mechanics truncation of the BBKGY hierarchy at the n-th level. We derive the
equations governing the evolution of mean field and two-point functions thus
identifying the terms corresponding to dissipation and noise. We discuss
possible applications of our formalism, the emergence of classical behaviour
and the connection to the decoherent histories framework.Comment: 25 pages, Late
Bayesian Probabilities and the Histories Algebra
We attempt a justification of a generalisation of the consistent histories
programme using a notion of probability that is valid for all complete sets of
history propositions. This consists of introducing Cox's axioms of probability
theory and showing that our candidate notion of probability obeys them. We also
give a generalisation of Bayes' theorem and comment upon how Bayesianism should
be useful for the quantum gravity/cosmology programmes.Comment: 10 pages, accepted by Int. J. Theo. Phys. Feb 200
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