330 research outputs found
Dirac's Constrained Hamiltonian Dynamics from an Unconstrained Dynamics
We derive the Hamilton equations of motion for a constrained system in the
form given by Dirac, by a limiting procedure, starting from the Lagrangean for
an unconstrained system. We thereby ellucidate the role played by the primary
constraints and their persistance in time.Comment: 10 page
Perfect and Imperfect Gauge Fixing
Gauge fixing may be done in different ways. We show that using the chain
structure to describe a constrained system, enables us to use either a perfect
gauge, in which all gauged degrees of freedom are determined; or an imperfect
gauge, in which some first class constraints remain as subsidiary conditions to
be imposed on the solutions of the equations of motion. We also show that the
number of constants of motion depends on the level in a constraint chain in
which the gauge fixing condition is imposed. The relativistic point particle,
electromagnetism and the Polyakov string are discussed as examples and perfect
or imperfect gauges are distinguished.Comment: 19 pages, no figur
Tensor Coordinates in Noncommutative Mechanics
A consistent classical mechanics formulation is presented in such a way that,
under quantization, it gives a noncommutative quantum theory with interesting
new features. The Dirac formalism for constrained Hamiltonian systems is
strongly used, and the object of noncommutativity plays
a fundamental rule as an independent quantity. The presented classical theory,
as its quantum counterpart, is naturally invariant under the rotation group
.Comment: 12 pages, Late
Hodge Duality Operation And Its Physical Applications On Supermanifolds
An appropriate definition of the Hodge duality operation on any
arbitrary dimensional supermanifold has been a long-standing problem. We define
a working rule for the Hodge duality operation on the -dimensional supermanifold parametrized by a couple of even (bosonic)
spacetime variables and a couple of Grassmannian (odd)
variables and of the Grassmann algebra. The Minkowski
spacetime manifold, hidden in the supermanifold and parametrized by , is chosen to be a flat manifold on which a two -dimensional
(2D) free Abelian gauge theory, taken as a prototype field theoretical model,
is defined. We demonstrate the applications of the above definition (and its
further generalization) for the discussion of the (anti-)co-BRST symmetries
that exist for the field theoretical models of 2D- (and 4D) free Abelian gauge
theories considered on the four - (and six )-dimensional
supermanifolds, respectively.Comment: LaTeX file, 25 pages, Journal-versio
Gravitational observables, intrinsic coordinates, and canonical maps
It is well known that in a generally covariant gravitational theory the
choice of spacetime scalars as coordinates yields phase-space observables (or
"invariants"). However their relation to the symmetry group of diffeomorphism
transformations has remained obscure. In a symmetry-inspired approach we
construct invariants out of canonically induced active gauge transformations.
These invariants may be intepreted as the full set of dynamical variables
evaluated in the intrinsic coordinate system. The functional invariants can
explicitly be written as a Taylor expansion in the coordinates of any observer,
and the coefficients have a physical and geometrical interpretation.
Surprisingly, all invariants can be obtained as limits of a family of canonical
transformations. This permits a short (again geometric) proof that all
invariants, including the lapse and shift, satisfy Poisson brackets that are
equal to the invariants of their corresponding Dirac brackets.Comment: 4 pages, to appear in Modern Physics Letters
BRST, anti-BRST and their geometry
We continue the comparison between the field theoretical and geometrical
approaches to the gauge field theories of various types, by deriving their
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST trasformation properties and
comparing them with the geometrical properties of the bundles and gerbes. In
particular, we provide the geometrical interpretation of the so--called
Curci-Ferrari conditions that are invoked for the absolute anticommutativity of
the BRST and anti-BRST symmetry transformations in the context of non-Abelian
1-form gauge theories as well as Abelian gauge theory that incorporates a
2-form gauge field. We also carry out the explicit construction of the 3-form
gauge fields and compare it with the geometry of 2--gerbes.Comment: A comment added. To appear in Jour. Phys. A: Mathemaical and
Theoretica
Investigating the eddy diffusivity concept in the coastal ocean
Author Posting. © American Meteorological Society, 2016. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2016): 2201-2218, doi:10.1175/JPO-D-16-0020.1.This paper aims to test the validity, utility, and limitations of the lateral eddy diffusivity concept in a coastal environment through analyzing data from coupled drifter and dye releases within the footprint of a high-resolution (800 m) high-frequency radar south of Martha’s Vineyard, Massachusetts. Specifically, this study investigates how well a combination of radar-based velocities and drifter-derived diffusivities can reproduce observed dye spreading over an 8-h time interval. A drifter-based estimate of an anisotropic diffusivity tensor is used to parameterize small-scale motions that are unresolved and underresolved by the radar system. This leads to a significant improvement in the ability of the radar to reproduce the observed dye spreading.IR, AK, and SL were supported by the NSF OCE Grant 1332646. IR was also supported by NASA Grant NNX14AH29G.2016-12-2
Constrained Dynamics of Universally Coupled Massive Spin 2-spin 0 Gravities
The 2-parameter family of massive variants of Einstein's gravity (on a
Minkowski background) found by Ogievetsky and Polubarinov by excluding lower
spins can also be derived using universal coupling. A Dirac-Bergmann
constrained dynamics analysis seems not to have been presented for these
theories, the Freund-Maheshwari-Schonberg special case, or any other massive
gravity beyond the linear level treated by Marzban, Whiting and van Dam. Here
the Dirac-Bergmann apparatus is applied to these theories. A few remarks are
made on the question of positive energy. Being bimetric, massive gravities have
a causality puzzle, but it appears soluble by the introduction and judicious
use of gauge freedom.Comment: 6 pages; Talk given at QG05, Cala Gonone (Italy), September 200
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