772 research outputs found
Noncommutative quantum mechanics: uniqueness of the functional description
The generalized Weyl transform of index is used to implement the
time-slice definition of the phase space path integral yielding the Feynman
kernel in the case of noncommutative quantum mechanics. As expected, this
representation for the Feynman kernel is not unique but labeled by the real
parameter . We succeed in proving that the -dependent
contributions disappear at the limit where the time slice goes to zero. This
proof of consistency turns out to be intricate because the Hamiltonian involves
products of noncommuting operators originating from the non-commutativity. The
antisymmetry of the matrix parameterizing the non-commutativity plays a key
role in the cancelation mechanism of the -dependent terms.Comment: 13 page
Einstein gravity as a 3D conformally invariant theory
We give an alternative description of the physical content of general
relativity that does not require a Lorentz invariant spacetime. Instead, we
find that gravity admits a dual description in terms of a theory where local
size is irrelevant. The dual theory is invariant under foliation preserving
3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume
(for the spatially compact case). Locally, this symmetry is identical to that
of Horava-Lifshitz gravity in the high energy limit but our theory is
equivalent to Einstein gravity. Specifically, we find that the solutions of
general relativity, in a gauge where the spatial hypersurfaces have constant
mean extrinsic curvature, can be mapped to solutions of a particular gauge
fixing of the dual theory. Moreover, this duality is not accidental. We provide
a general geometric picture for our procedure that allows us to trade foliation
invariance for conformal invariance. The dual theory provides a new proposal
for the theory space of quantum gravity.Comment: 27 pages. Published version (minor changes and corrections
Dynamical Compactification and Inflation in Einstein-Yang-Mills Theory with Higher Derivative Coupling
We study cosmology of the Einstein-Yang-Mills theory in ten dimensions with a
quartic term in the Yang-Mills field strength. We obtain analytically a class
of cosmological solutions in which the extra dimensions are static and the
scale factor of the four-dimensional Friedmann-Lemaitre-Robertson-Walker metric
is an exponential function of time. This means that the model can explain
inflation. Then we look for solutions that describe dynamical compactification
of the extra dimensions. The effective cosmological constant in the
four-dimensional universe is determined from the gravitational coupling,
ten-dimensional cosmological constant, gauge coupling and higher derivative
coupling. By numerical integration, the solution with is found to
behave as a matter-dominated universe which asymptotically approaches flat
space-time, while the solution with a non-vanishing approaches de
Sitter space-time in the asymptotic future.Comment: 30 pages, 7 figure
Exact General Relativistic Thick Disks
A method to construct exact general relativistic thick disks that is a simple
generalization of the ``displace, cut and reflect'' method commonly used in
Newtonian, as well as, in Einstein theory of gravitation is presented. This
generalization consists in the addition of a new step in the above mentioned
method. The new method can be pictured as a ``displace, cut, {\it fill} and
reflect'' method. In the Newtonian case, the method is illustrated in some
detail with the Kuzmin-Toomre disk. We obtain a thick disk with acceptable
physical properties. In the relativistic case two solutions of the Weyl
equations, the Weyl gamma metric (also known as Zipoy-Voorhees metric) and the
Chazy-Curzon metric are used to construct thick disks. Also the Schwarzschild
metric in isotropic coordinates is employed to construct another family of
thick disks. In all the considered cases we have non trivial ranges of the
involved parameter that yield thick disks in which all the energy conditions
are satisfied.Comment: 11 pages, RevTex, 9 eps figs. Accepted for publication in PR
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
Compact Lattice QED and the Coulomb Potential
The potential energy of a static charge distribution on a lattice is
rigorously computed in the standard compact quantum electrodynamic model. The
method used follows closely that of Weyl for ordinary quantum electrodynamics
in continuous space-time. The potential energy of the static charge
distribution is independent of temperature and can be calculated from the
lattice version of Poisson's equation. It is the usual Coulomb potential.Comment: 6 pages, includes one figure in Topdrawer, NUB 3054/9
Periastron shift in Weyl class spacetimes
The periastron position advance for geodesic motion in axially symmetric
solutions of the Einstein field equations belonging to the Weyl class of vacuum
solutions is investigated. Explicit examples corresponding to either static
solutions (single Chazy-Curzon, Schwarzschild and a pair of them), or
stationary solution (single rotating Chazy-Curzon and Kerr black hole) are
discussed. The results are then applied to the case of S2-SgrA binary
system of which the periastron position advance will be soon measured with a
great accuracy.Comment: To appear on General Relativity and Gravitation, vol. 37, 200
When Black Holes Meet Kaluza-Klein Bubbles
We explore the physical consequences of a recently discovered class of exact
solutions to five dimensional Kaluza-Klein theory. We find a number of
surprising features including: (1) In the presence of a Kaluza-Klein bubble,
there are arbitrarily large black holes with topology S^3. (2) In the presence
of a black hole or a black string, there are expanding bubbles (with de Sitter
geometry) which never reach null infinity. (3) A bubble can hold two black
holes of arbitrary size in static equilibrium. In particular, two large black
holes can be close together without merging to form a single black hole.Comment: 23 pages, 5 figures, v2: few comments on stability modifie
Wormhole geometries supported by a nonminimal curvature-matter coupling
Wormhole geometries in curvature-matter coupled modified gravity are
explored, by considering an explicit nonminimal coupling between an arbitrary
function of the scalar curvature, R, and the Lagrangian density of matter. It
is the effective stress-energy tensor containing the coupling between matter
and the higher order curvature derivatives that is responsible for the null
energy condition violation, and consequently for supporting the respective
wormhole geometries. The general restrictions imposed by the null energy
condition violation are presented in the presence of a nonminimal R-matter
coupling. Furthermore, obtaining exact solutions to the gravitational field
equations is extremely difficult due to the nonlinearity of the equations,
although the problem is mathematically well-defined. Thus, we outline several
approaches for finding wormhole solutions, and deduce an exact solution by
considering a linear R nonmiminal curvature-matter coupling and by considering
an explicit monotonically decreasing function for the energy density. Although
it is difficult to find exact solutions of matter threading the wormhole
satisfying the energy conditions at the throat, an exact solution is found
where the nonminimal coupling does indeed minimize the violation of the null
energy condition of normal matter at the throat.Comment: 8 pages, 3 figures. V2: 9 pages, error and typos corrected;
discussion and references added; to appear in PR
Applications of quantum integrable systems
We present two applications of quantum integrable systems. First, we predict
that it is possible to generate high harmonics from solid state devices by
demostrating that the emission spectrum for a minimally coupled laser field of
frequency to an impurity system of a quantum wire, contains multiples
of the incoming frequency. Second, evaluating expressions for the conductance
in the high temperature regime we show that the caracteristic filling fractions
of the Jain sequence, which occur in the fractional quantum Hall effect, can be
obtained from quantum wires which are described by minimal affine Toda field
theories.Comment: 25 pages of LaTex, 4 figures, based on talk at the 6-th international
workshop on conformal field theories and integrable models, (Chernogolovka,
September 2002
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