532 research outputs found
Noncommutative Coordinates Invariant under Rotations and Lorentz Transformations
Dynamics with noncommutative coordinates invariant under three dimensional
rotations or, if time is included, under Lorentz transformations is developed.
These coordinates turn out to be the boost operators in SO(1,3) or in SO(2,3)
respectively. The noncommutativity is governed by a mass parameter . The
principal results are: (i) a modification of the Heisenberg algebra for
distances smaller than 1/M, (ii) a lower limit, 1/M, on the localizability of
wave packets, (iii) discrete eigenvalues of coordinate operator in timelike
directions, and (iv) an upper limit, , on the mass for which free field
equations have solutions. Possible restrictions on small black holes is
discussed.Comment: 14 pages; LaTex using JHEP3.cl
Probing the Noncommutative Standard Model at Hadron Colliders
We study collider signals for the noncommutative extension of the standard
model using the Seiberg-Witten maps for SU(3)_C x SU(2)_L x U(1)_Y to first
order in the noncommutativity parameters theta_munu. In particular, we
investigate the ensitivity of Z-gamma-production at the Tevatron and the LHC to
the components of theta_munu. We discuss the range of validity of this
approximation and estimate exclusion limits from a Monte Carlo simulation.Comment: 18 pages LaTeX, 23 figures. Slightly expanded introduction and
additional references. Accepted for publication in Physical Review
Noncommuting spherical coordinates
Restricting the states of a charged particle to the lowest Landau level
introduces a noncommutativity between Cartesian coordinate operators. This idea
is extended to the motion of a charged particle on a sphere in the presence of
a magnetic monopole. Restricting the dynamics to the lowest energy level
results in noncommutativity for angular variables and to a definition of a
noncommuting spherical product. The values of the commutators of various
angular variables are not arbitrary but are restricted by the discrete
magnitude of the magnetic monopole charge. An algebra, isomorphic to angular
momentum, appears. This algebra is used to define a spherical star product.
Solutions are obtained for dynamics in the presence of additional angular
dependent potentials.Comment: 5 pages, RevTex4 fil
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
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
Born series and unitarity in noncommutative quantum mechanics
This paper is dedicated to present model independent results for
noncommutative quantum mechanics. We determine sufficient conditions for the
convergence of the Born series and, in the sequel, unitarity is proved in full
generality.Comment: 9 page
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
Caldirola-Kanai Oscillator in Classical Formulation of Quantum Mechanics
The quadrature distribution for the quantum damped oscillator is introduced
in the framework of the formulation of quantum mechanics based on the
tomography scheme. The probability distribution for the coherent and Fock
states of the damped oscillator is expressed explicitly in terms of Gaussian
and Hermite polynomials, correspondingly.Comment: LaTeX, 5 pages, 1 Postscript figure, Contribution to the VIII
International Conference on Symmetry Methods in Physics, Dubna 1997, to be
published in the Proceedings of the Conferenc
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
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