2,209 research outputs found
Rosenfeld, Bergmann, Dirac and the Invention of Constrained Hamiltonian Dynamics
In a paper appearing in Annalen der Physik in 1930 Leon Rosenfeld invented
the first procedure for producing Hamiltonian constraints. He displayed and
correctly distinguished the vanishing Hamiltonian generator of time evolution,
and the vanishing generator of gauge transformations for general relativity
with Dirac electron and electrodynamic field sources. Though he did not do so,
had he chosen one of his tetrad fields to be normal to his spacetime foliation,
he would have anticipated by almost thirty years the general relativisitic
Hamiltonian first published by Paul Dirac.Comment: 5 pages, to appear in the Proceedings of the Eleventh Marcel
Grossmann Meetin
A generalized Schroedinger equation for loop quantum cosmology
A temporally discrete Schroedinger time evolution equation is proposed for
isotropic quantum cosmology coupled to a massless scalar source. The approach
employs dynamically determined intrinsic time and produces the correct
semiclassical limit.Comment: 5 pages, to appear in the Proceedings of the Eleventh Marcel
Grossmann Meetin
Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories
We study spacetime diffeomorphisms in Hamiltonian and Lagrangian formalisms
of generally covariant systems. We show that the gauge group for such a system
is characterized by having generators which are projectable under the Legendre
map. The gauge group is found to be much larger than the original group of
spacetime diffeomorphisms, since its generators must depend on the lapse
function and shift vector of the spacetime metric in a given coordinate patch.
Our results are generalizations of earlier results by Salisbury and
Sundermeyer. They arise in a natural way from using the requirement of
equivalence between Lagrangian and Hamiltonian formulations of the system, and
they are new in that the symmetries are realized on the full set of phase space
variables. The generators are displayed explicitly and are applied to the
relativistic string and to general relativity.Comment: 12 pages, no figures; REVTeX; uses multicol,fancyheadings,eqsecnum;
to appear in Phys. Rev.
Multiple acid pathways in Casco Bay: Implications for the next 25 years (2015 State of the Bay Presentation)
https://digitalcommons.usm.maine.edu/cbep-presentations/1020/thumbnail.jp
Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity
We show how to treat the constraints and reality conditions in the
-ADM (Ashtekar) formulation of general relativity, for the case of a
vacuum spacetime with a cosmological constant. We clarify the difference
between the reality conditions on the metric and on the triad. Assuming the
triad reality condition, we find a new variable, allowing us to solve the gauge
constraint equations and the reality conditions simultaneously.Comment: LaTeX file, 12 pages, no figures; to appear in Classical and Quantum
Gravit
Temporal and spatial dynamics of CO2 air-sea flux in the Gulf of Maine
Ocean surface layer carbon dioxide (CO2) data collected in the Gulf of Maine from 2004 to 2008 are presented. Monthly shipboard observations are combined with additional higherâresolution CO2 observations to characterize CO2 fugacity ( fCO2) and CO2 flux over hourly to interannual time scales. Observed fCO2 andCO2 flux dynamics are dominated by a seasonal cycle, with a large spring influx of CO2 and a fallâtoâwinter efflux back to the atmosphere. The temporal results at inner, middle, and outer shelf locations are highly correlated, and observed spatial variability is generally small relative to the monthly to seasonal temporal changes. The averaged annual flux is in near balance and is a net source of carbon to the atmosphere over 5 years, with a value of +0.38 mol mâ2 yrâ1. However, moderate interannual variation is also observed, where years 2005 and 2007 represent cases of regional source (+0.71) and sink (â0.11) anomalies. We use moored daily CO2 measurements to quantify aliasing due to temporal undersampling, an important error budget term that is typically unresolved. The uncertainty of our derived annual flux measurement is ±0.26 mol mâ2 yrâ1 and is dominated by this aliasing term. Comparison of results to the neighboring Middle and South Atlantic Bight coastal shelf systems indicates that the Gulf of Maine exhibits a similar annual cycle and range of oceanic fCO2 magnitude but differs in the seasonal phase. It also differs by enhanced fCO2 controls by factors other than temperatureâdriven solubility, including biological drawdown, fallâtoâwinter vertical mixing, and river runoff
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