414 research outputs found
Noncommutative gauge fields coupled to noncommutative gravity
We present a noncommutative (NC) version of the action for vielbein gravity
coupled to gauge fields. Noncommutativity is encoded in a twisted star product
between forms, with a set of commuting background vector fields defining the
(abelian) twist. A first order action for the gauge fields avoids the use of
the Hodge dual. The NC action is invariant under diffeomorphisms and twisted
gauge transformations. The Seiberg-Witten map, adapted to our geometric setting
and generalized for an arbitrary abelian twist, allows to re-express the NC
action in terms of classical fields: the result is a deformed action, invariant
under diffeomorphisms and usual gauge transformations. This deformed action is
a particular higher derivative extension of the Einstein-Hilbert action coupled
to Yang-Mills fields, and to the background vector fields defining the twist.
Here noncommutativity of the original NC action dictates the precise form of
this extension. We explicitly compute the first order correction in the NC
parameter of the deformed action, and find that it is proportional to cubic
products of the gauge field strength and to the symmetric anomaly tensor
D_{IJK}.Comment: 18 pages, LaTe
Noncommutative deformation of four dimensional Einstein gravity
We construct a model for noncommutative gravity in four dimensions, which
reduces to the Einstein-Hilbert action in the commutative limit. Our proposal
is based on a gauge formulation of gravity with constraints. While the action
is metric independent, the constraints insure that it is not topological. We
find that the choice of the gauge group and of the constraints are crucial to
recover a correct deformation of standard gravity. Using the Seiberg-Witten map
the whole theory is described in terms of the vierbeins and of the Lorentz
transformations of its commutative counterpart. We solve explicitly the
constraints and exhibit the first order noncommutative corrections to the
Einstein-Hilbert action.Comment: LaTex, 11 pages, comments added, to appear in Classical and Quantum
Gravit
Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space
Classical mechanics is formulated in complex Hilbert space with the
introduction of a commutative product of operators, an antisymmetric bracket,
and a quasidensity operator. These are analogues of the star product, the Moyal
bracket, and the Wigner function in the phase space formulation of quantum
mechanics. Classical mechanics can now be viewed as a deformation of quantum
mechanics. The forms of semiquantum approximations to classical mechanics are
indicated.Comment: 10 pages, Latex2e file, references added, minor clarifications mad
Wigner Trajectory Characteristics in Phase Space and Field Theory
Exact characteristic trajectories are specified for the time-propagating
Wigner phase-space distribution function. They are especially simple---indeed,
classical---for the quantized simple harmonic oscillator, which serves as the
underpinning of the field theoretic Wigner functional formulation introduced.
Scalar field theory is thus reformulated in terms of distributions in field
phase space. Applications to duality transformations in field theory are
discussed.Comment: 9 pages, LaTex2
Group Theory and Quasiprobability Integrals of Wigner Functions
The integral of the Wigner function of a quantum mechanical system over a
region or its boundary in the classical phase plane, is called a
quasiprobability integral. Unlike a true probability integral, its value may
lie outside the interval [0,1]. It is characterized by a corresponding
selfadjoint operator, to be called a region or contour operator as appropriate,
which is determined by the characteristic function of that region or contour.
The spectral problem is studied for commuting families of region and contour
operators associated with concentric disks and circles of given radius a. Their
respective eigenvalues are determined as functions of a, in terms of the
Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in
Hilbert space carrying the positive discrete series representations of the
algebra su(1,1)or so(2,1). The explicit relation between the spectra of
operators associated with disks and circles with proportional radii, is given
in terms of the dicrete variable Meixner polynomials.Comment: 11 pages, latex fil
Conformal Covariantization of Moyal-Lax Operators
A covariant approach to the conformal property associated with Moyal-Lax
operators is given. By identifying the conformal covariance with the second
Gelfand-Dickey flow, we covariantize Moyal-Lax operators to construct the
primary fields of one-parameter deformation of classical -algebras.Comment: 13 pages, Revtex, no figures, v.2: typos corrected, references added
and conclusion modifie
Predator-Prey Interactions between Droplets Driven by Nonreciprocal Oil Exchange
Chemotactic interactions are ubiquitous in nature and can lead to
nonreciprocal and complex emergent behavior in multibody systems. Here we show
how chemotactic signaling between microscale oil droplets of different
chemistries in micellar surfactant solutions can result in predator-prey-like
chasing interactions. The interactions and dynamic self-organization result
from the net directional, micelle-mediated transport of oil between emulsion
droplets of differing composition and are powered by the free energy of mixing.
The nonreciprocal behavior occurs in a wide variety of oil and surfactant
conditions, and we systematically elucidate chemical design rules for tuning
the interactions between droplets by varying oil and surfactant chemical
structure and concentration. Through integration of experiment and simulation,
we also investigate the active behavior and dynamic reorganization of
multi-droplet clusters. Our findings demonstrate how chemically-minimal systems
can be designed with controllable, non-reciprocal chemotactic interactions to
generate emergent self-organization and collective behaviors reminiscent of
biological systems
Unambiguous quantization from the maximum classical correspondence that is self-consistent: the slightly stronger canonical commutation rule Dirac missed
Dirac's identification of the quantum analog of the Poisson bracket with the
commutator is reviewed, as is the threat of self-inconsistent overdetermination
of the quantization of classical dynamical variables which drove him to
restrict the assumption of correspondence between quantum and classical Poisson
brackets to embrace only the Cartesian components of the phase space vector.
Dirac's canonical commutation rule fails to determine the order of noncommuting
factors within quantized classical dynamical variables, but does imply the
quantum/classical correspondence of Poisson brackets between any linear
function of phase space and the sum of an arbitrary function of only
configuration space with one of only momentum space. Since every linear
function of phase space is itself such a sum, it is worth checking whether the
assumption of quantum/classical correspondence of Poisson brackets for all such
sums is still self-consistent. Not only is that so, but this slightly stronger
canonical commutation rule also unambiguously determines the order of
noncommuting factors within quantized dynamical variables in accord with the
1925 Born-Jordan quantization surmise, thus replicating the results of the
Hamiltonian path integral, a fact first realized by E. H. Kerner. Born-Jordan
quantization validates the generalized Ehrenfest theorem, but has no inverse,
which disallows the disturbing features of the poorly physically motivated
invertible Weyl quantization, i.e., its unique deterministic classical "shadow
world" which can manifest negative densities in phase space.Comment: 12 pages, Final publication in Foundations of Physics; available
online at http://www.springerlink.com/content/k827666834140322
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