575 research outputs found
Gravitational Constraint Combinations Generate a Lie Algebra
We find a first--order partial differential equation whose solutions are all
ultralocal scalar combinations of gravitational constraints with Abelian
Poisson brackets between themselves. This is a generalisation of the Kucha\v{r}
idea of finding alternative constraints for canonical gravity. The new scalars
may be used in place of the hamiltonian constraint of general relativity and,
together with the usual momentum constraints, replace the Dirac algebra for
pure gravity with a true Lie algebra: the semidirect product of the Abelian
algebra of the new constraint combinations with the algebra of spatial
diffeomorphisms.Comment: 10 pages, latex, submitted to Classical and Quantum Gravity. Section
3 is expanded and an additional solution provided, minor errors correcte
Action functionals of single scalar fields and arbitrary--weight gravitational constraints that generate a genuine Lie algebra
We discuss the issue initiated by Kucha\v{r} {\it et al}, of replacing the
usual Hamiltonian constraint by alternative combinations of the gravitational
constraints (scalar densities of arbitrary weight), whose Poisson brackets
strongly vanish and cast the standard constraint-system for vacuum gravity into
a form that generates a true Lie algebra. It is shown that any such
combination---that satisfies certain reality conditions---may be derived from
an action principle involving a single scalar field and a single Lagrange
multiplier with a non--derivative coupling to gravity.Comment: 26 pages, plain TE
Fluid dynamics in flexible tubes: An application to the study of the pulmonary circulation
Based on an analysis of unsteady, viscous flow through distensible tubes, a lumped-parameter model for the dynamics of blood flow through the pulmonary vascular bed was developed. The model is nonlinear, incorporating the variation of flow resistance with transmural pressure. Solved using a hybrid computer, the model yields information concerning the time-dependent behavior of blood pressures, flow rates, and volumes in each important class of vessels in each lobe of each lung in terms of the important physical and environmental parameters. Simulations of twenty abnormal or pathological situations of interest in environmental physiology and clinical medicine were performed. The model predictions agree well with physiological data
Mass Superselection, Canonical Gauge Transformations, and Asymptotically Flat Variational Principles
The phase space reduction of Schwarzschild black holes by Thiemann and
Kastrup and by Kucha\v{r} is reexamined from a different perspective on gauge
freedom. This perspective introduces additional gauge transformations which
correspond to asymptotically nontrivial diffeomorphisms. Various subtleties
concerning variational principles for asymptotically flat systems are addressed
which allow us to avoid the usual conclusion that treating such transformations
as gauge implies the vanishing of corresponding total charges. Instead,
superselection rules are found for the (nonvanishing) ADM mass at the
asymptotic boundaries. The addition of phenomenological clocks at each
asymptotic boundary is also studied and compared with the `parametrization
clocks' of Kucha\v{r}.Comment: 15 pages, ReVTeX, Minor changes made in response to referee's
commment
Canonical Formulation of pp-waves
We construct a Hamiltonian formulation for the class of plane-fronted
gravitational waves with parallel rays (pp-waves). Because of the existence of
a light-like Killing vector, the dynamics is effectively reduced to a 2+1
evolution with "time" chosen to be light-like. In spite of the vanishing action
this allows us to geometrically identify a symplectic form as well as dynamical
Hamiltonian, thus casting the system into canonical form.Comment: To appear in the "Obregon Festschrift
Free fields via canonical transformations of matter-coupled 2D dilaton gravity models
It is shown that the 1+1-dimensional matter-coupled Jackiw-Teitelboim model
and the model with an exponential potential can be converted by means of
appropriate canonical transformations into a bosonic string theory propagating
on a flat target space with an indefinite signature. This makes it possible to
consistently quantize these models in the functional Schroedinger
representation thus generalizing recent results on CGHS theory.Comment: 15 pages, Late
Functional Evolution of Free Quantum Fields
We consider the problem of evolving a quantum field between any two (in
general, curved) Cauchy surfaces. Classically, this dynamical evolution is
represented by a canonical transformation on the phase space for the field
theory. We show that this canonical transformation cannot, in general, be
unitarily implemented on the Fock space for free quantum fields on flat
spacetimes of dimension greater than 2. We do this by considering time
evolution of a free Klein-Gordon field on a flat spacetime (with toroidal
Cauchy surfaces) starting from a flat initial surface and ending on a generic
final surface. The associated Bogolubov transformation is computed; it does not
correspond to a unitary transformation on the Fock space. This means that
functional evolution of the quantum state as originally envisioned by Tomonaga,
Schwinger, and Dirac is not a viable concept. Nevertheless, we demonstrate that
functional evolution of the quantum state can be satisfactorily described using
the formalism of algebraic quantum field theory. We discuss possible
implications of our results for canonical quantum gravity.Comment: 21 pages, RevTeX, minor improvements in exposition, to appear in
Classical and Quantum Gravit
The physical hamiltonian in nonperturbative quantum gravity
A quantum hamiltonian which evolves the gravitational field according to time
as measured by constant surfaces of a scalar field is defined through a
regularization procedure based on the loop representation, and is shown to be
finite and diffeomorphism invariant. The problem of constructing this
hamiltonian is reduced to a combinatorial and algebraic problem which involves
the rearrangements of lines through the vertices of arbitrary graphs. This
procedure also provides a construction of the hamiltonian constraint as a
finite operator on the space of diffeomorphism invariant states as well as a
construction of the operator corresponding to the spatial volume of the
universe.Comment: Latex, 11 pages, no figures, CGPG/93/
ADM Worldvolume Geometry
We describe the dynamics of a relativistic extended object in terms of the
geometry of a configuration of constant time. This involves an adaptation of
the ADM formulation of canonical general relativity. We apply the formalism to
the hamiltonian formulation of a Dirac-Nambu-Goto relativistic extended object
in an arbitrary background spacetime.Comment: 4 pages, Latex. Uses espcrc2.sty To appear in the proceedings of the
Third Conference on Constrained Dynamics and Quantum Gravity, September,
1999. To appear in Nuclear Physics B (Proceedings Supplement
Hazard alerting and situational awareness in advanced air transport cockpits
Advances in avionics and display technology have significantly changed the cockpit environment in current 'glass cockpit' aircraft. Recent developments in display technology, on-board processing, data storage, and datalinked communications are likely to further alter the environment in second and third generation 'glass cockpit' aircraft. The interaction of advanced cockpit technology with human cognitive performance has been a major area of activity within the MIT Aeronautical Systems Laboratory. This paper presents an overview of the MIT Advanced Cockpit Simulation Facility. Several recent research projects are briefly reviewed and the most important results are summarized
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