533 research outputs found
Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections
In this paper we deal with the issue of Lorentz symmetry breaking in quantum
field theories formulated in a non-commutative space-time. We show that, unlike
in some recente analysis of quantum gravity effects, supersymmetry does not
protect the theory from the large Lorentz violating effects arising from the
loop corrections. We take advantage of the non-commutative Wess-Zumino model to
illustrate this point.Comment: 9 pages, revtex4. Corrected references. Version published in PR
Newton's law in an effective non commutative space-time
The Newtonian Potential is computed exactly in a theory that is fundamentally
Non Commutative in the space-time coordinates. When the dispersion for the
distribution of the source is minimal (i.e. it is equal to the non commutative
parameter ), the behavior for large and small distances is analyzed.Comment: 5 page
On the propagation of semiclassical Wigner functions
We establish the difference between the propagation of semiclassical Wigner
functions and classical Liouville propagation. First we re-discuss the
semiclassical limit for the propagator of Wigner functions, which on its own
leads to their classical propagation. Then, via stationary phase evaluation of
the full integral evolution equation, using the semiclassical expressions of
Wigner functions, we provide the correct geometrical prescription for their
semiclassical propagation. This is determined by the classical trajectories of
the tips of the chords defined by the initial semiclassical Wigner function and
centered on their arguments, in contrast to the Liouville propagation which is
determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the
one set to print and differs from the previous one (07 Nov 2001) by the
addition of two references, a few extra words of explanation and an augmented
figure captio
Physical Wigner functions
In spite of their potential usefulness, the characterizations of Wigner
functions for Bose and Fermi statistics given by O'Connell and Wigner himself
almost thirty years ago has drawn little attention. With an eye towards
applications in quantum chemistry, we revisit and reformulate them in a more
convenient way.Comment: Latex, 10 page
Quantum deformation of the Dirac bracket
The quantum deformation of the Poisson bracket is the Moyal bracket. We
construct quantum deformation of the Dirac bracket for systems which admit
global symplectic basis for constraint functions. Equivalently, it can be
considered as an extension of the Moyal bracket to second-class constraints
systems and to gauge-invariant systems which become second class when
gauge-fixing conditions are imposed.Comment: 18 pages, REVTe
On calculating the mean values of quantum observables in the optical tomography representation
Given a density operator the optical tomography map defines a
one-parameter set of probability distributions on the real line allowing to reconstruct . We
introduce a dual map from the special class of quantum observables
to a special class of generalized functions such that the
mean value is given by the formula
. The class
includes all the symmetrized polynomials of canonical variables
and .Comment: 8 page
Maximal Bell's Inequality Violation for Non Maximal Entanglement
Bell's inequality violation (BIQV) for correlations of polarization is
studied for a {\it product} state of two two-mode squeezed vacuum (TMSV)
states. The violation allowed is shown to attain its maximal limit for all
values of the squeezing parameter, . We show via an explicit example
that a state whose entanglement is not maximal allow maximal BIQV. The Wigner
function of the state is non negative and the average value of either
polarization is nil.Comment: 8 pages, latex, no figure
The Moyal Bracket in the Coherent States framework
The star product and Moyal bracket are introduced using the coherent states
corresponding to quantum systems with non-linear spectra. Two kinds of coherent
state are considered. The first kind is the set of Gazeau-Klauder coherent
states and the second kind are constructed following the Perelomov-Klauder
approach. The particular case of the harmonic oscillator is also discussed.Comment: 13 page
Noncommutative Quantum Cosmology
We consider noncommutative quantum cosmology in the case of the low-energy
string effective theory. Exacts solutions are found and compared with the
commutative case.The Noncommutative quantum cosmology is considered in the case
of the low-energy string effective theory. Exacts solutions are found and
compared with the commutative case.Comment: Revtex4, 3 pages, 2 figures, to appear in Gen.Rel.Gra
On the B\"acklund Transformation for the Moyal Korteweg-de Vries Hierarchy
We study the B\"acklund symmetry for the Moyal Korteweg-de Vries (KdV)
hierarchy based on the Kuperschmidt-Wilson Theorem associated with second
Gelfand-Dickey structure with respect to the Moyal bracket, which generalizes
the result of Adler for the ordinary KdV.Comment: 9 pages, Revte
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