501 research outputs found
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
Quantum Logic and the Histories Approach to Quantum Theory
An extended analysis is made of the Gell-Mann and Hartle axioms for a
generalised `histories' approach to quantum theory. Emphasis is placed on
finding equivalents of the lattice structure that is employed in standard
quantum logic. Particular attention is given to `quasi-temporal' theories in
which the notion of time-evolution is less rigid than in conventional
Hamiltonian physics; theories of this type are expected to arise naturally in
the context of quantum gravity and quantum field theory in a curved space-time.
The quasi-temporal structure is coded in a partial semi-group of `temporal
supports' that underpins the lattice of history propositions. Non-trivial
examples include quantum field theory on a non globally-hyperbolic spacetime,
and a simple cobordism approach to a theory of quantum topology.
It is shown how the set of history propositions in standard quantum theory
can be realised in such a way that each history proposition is represented by a
genuine projection operator. This provides valuable insight into the possible
lattice structure in general history theories, and also provides a number of
potential models for theories of this type.Comment: TP/92-93/39 36 pages + one page of diagrams (I could email Apple
laser printer postscript file for anyone who is especially keen
Diffeomorphisms as Symplectomorphisms in History Phase Space: Bosonic String Model
The structure of the history phase space of a covariant field system
and its history group (in the sense of Isham and Linden) is analyzed on an
example of a bosonic string. The history space includes the time map
from the spacetime manifold (the two-sheet) to a
one-dimensional time manifold as one of its configuration variables. A
canonical history action is posited on such that its restriction to
the configuration history space yields the familiar Polyakov action. The
standard Dirac-ADM action is shown to be identical with the canonical history
action, the only difference being that the underlying action is expressed in
two different coordinate charts on . The canonical history action
encompasses all individual Dirac-ADM actions corresponding to different choices
of foliating . The history Poisson brackets of spacetime fields
on induce the ordinary Poisson brackets of spatial fields in the
instantaneous phase space of the Dirac-ADM formalism. The
canonical history action is manifestly invariant both under spacetime
diffeomorphisms Diff and temporal diffeomorphisms Diff. Both of
these diffeomorphisms are explicitly represented by symplectomorphisms on the
history phase space . The resulting classical history phase space
formalism is offered as a starting point for projection operator quantization
and consistent histories interpretation of the bosonic string model.Comment: 45 pages, no figure
Topos theory and `neo-realist' quantum theory
Topos theory, a branch of category theory, has been proposed as mathematical
basis for the formulation of physical theories. In this article, we give a
brief introduction to this approach, emphasising the logical aspects. Each
topos serves as a `mathematical universe' with an internal logic, which is used
to assign truth-values to all propositions about a physical system. We show in
detail how this works for (algebraic) quantum theory.Comment: 22 pages, no figures; contribution for Proceedings of workshop
"Recent Developments in Quantum Field Theory", MPI MIS Leipzig, July 200
Space-time modeling of soil moisture: Stochastic rainfall forcing with heterogeneous vegetation
The present paper complements that of Isham et al. (2005), who introduced a space-time soil moisture model driven by stochastic space-time rainfall forcing with homogeneous vegetation and in the absence of topographical landscape effects. However, the spatial variability of vegetation may significantly modify the soil moisture dynamics with important implications for hydrological modeling. In the present paper, vegetation heterogeneity is incorporated through a two dimensional Poisson process representing the coexistence of two functionally different types of plants (e.g., trees and grasses). The space-time statistical structure of relative soil moisture is characterized through its covariance function which depends on soil, vegetation, and rainfall patterns. The statistical properties of the soil moisture process averaged in space and time are also investigated. These properties are especially important for any modeling that aggregates soil moisture characteristics over a range of spatial and temporal scales. It is found that particularly at small scales, vegetation heterogeneity has a significant impact on the averaged process as compared with the uniform vegetation case. Also, averaging in space considerably smoothes the soil moisture process, but in contrast, averaging in time up to 1 week leads to little change in the variance of the averaged process
Effective approach to the problem of time: general features and examples
The effective approach to quantum dynamics allows a reformulation of the
Dirac quantization procedure for constrained systems in terms of an
infinite-dimensional constrained system of classical type. For semiclassical
approximations, the quantum constrained system can be truncated to finite size
and solved by the reduced phase space or gauge-fixing methods. In particular,
the classical feasibility of local internal times is directly generalized to
quantum systems, overcoming the main difficulties associated with the general
problem of time in the semiclassical realm. The key features of local internal
times and the procedure of patching global solutions using overlapping
intervals of local internal times are described and illustrated by two quantum
mechanical examples. Relational evolution in a given choice of internal time is
most conveniently described and interpreted in a corresponding choice of gauge
at the effective level and changing the internal clock is, therefore,
essentially achieved by a gauge transformation. This article complements the
conceptual discussion in arXiv:1009.5953.Comment: 42 pages, 9 figures; v2: streamlined discussions, more compact
manuscrip
A Kucha\v{r} Hypertime Formalism For Cylindrically Symmetric Spacetimes With Interacting Scalar Fields
The Kucha\v{r} canonical transformation for vacuum geometrodynamics in the
presence of cylindrical symmetry is applied to a general non-vacuum case. The
resulting constraints are highly non-linear and non-local in the momenta
conjugate to the Kucha\v{r} embedding variables. However, it is demonstrated
that the constraints can be solved for these momenta and thus the dynamics of
cylindrically symmetric models can be cast in a form suitable for the
construction of a hypertime functional Schr\"odinger equation.Comment: 5 pages, LaTeX, UBCTP-93-02
Population biology of multispecies helminth infection: interspecific interactions and parasite distribution
Despite evidence for the existence of interspecific interactions between helminth species, there has been no theoretical exploration of their effect on the distribution of the parasite species in a host population. We use a deterministic model for the accumulation and loss of adult worms of 2 interacting helminth species to motivate an individual-based stochastic model. The mean worm burden and variance: mean ratio (VMR) of each species, and the correlation between the two species are used to describe the distribution within different host age classes. We find that interspecific interactions can produce convex age-intensity profiles and will impact the level of aggregation (as measured by the VMR). In the absence of correlated exposure, the correlation in older age classes may be close to zero when either intra- or interspecific synergistic effects are strong. We therefore suggest examining the correlation between species in young hosts as a possible means of identifying interspecific interaction. The presence of correlation between the rates of exposure makes the interpretation of correlations between species more difficult. Finally we show that in the absence of interaction, strong positive correlations are generated by averaging across most age classes
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