460 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
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
On the concepts of radial and angular kinetic energies
We consider a general central-field system in D dimensions and show that the
division of the kinetic energy into radial and angular parts proceeds
differently in the wavefunction picture and the Weyl-Wigner phase-space
picture. Thus, the radial and angular kinetic energies are different quantities
in the two pictures, containing different physical information, but the
relation between them is well defined. We discuss this relation and illustrate
its nature by examples referring to a free particle and to a ground-state
hydrogen atom.Comment: 10 pages, 2 figures, accepted by Phys. Rev.
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
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
Uncertainty inequalities as entanglement criteria for negative partial-transpose states
In this Letter, we show that the fulfillment of uncertainty relations is a
sufficient criterion for a quantum-mechanically permissible state. We
specifically construct two pseudo-spin observables for an arbitrary
non-positive Hermitian matrix whose uncertainty relation is violated. This
method enables us to systematically derive separability conditions for all
negative partial-transpose states in experimentally accessible forms. In
particular, generalized entanglement criteria are derived from the
Schrodinger-Robertson inequalities for bipartite continuous-variable states.Comment: 4 pages, published version with minor change
Phenomenology of Noncommutative Field Theories
Experimental limits on the violation of four-dimensional Lorentz invariance
imply that noncommutativity among ordinary spacetime dimensions must be small.
In this talk, I review the most stringent bounds on noncommutative field
theories and suggest a possible means of evading them: noncommutativity may be
restricted to extra, compactified spatial dimensions. Such theories have a
number of interesting features, including Abelian gauge fields whose
Kaluza-Klein excitations have self couplings. We consider six-dimensional QED
in a noncommutative bulk, and discuss the collider signatures of the model.Comment: 7 pages RevTeX, 4 eps figures, Invited plenary talk, IX Mexican
Workshop on Particles and Fields, November 17-22, 2003, Universidad de
Colima, Mexic
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