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 $M$. 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, $M$, 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 $\hat \rho$ the optical tomography map defines a one-parameter set of probability distributions $w_{\hat \rho}(X,\phi),\ \phi \in [0,2\pi),$ on the real line allowing to reconstruct $\hat \rho$. We introduce a dual map from the special class $\mathcal A$ of quantum observables $\hat a$ to a special class of generalized functions $a(X,\phi)$ such that the mean value $_{\hat \rho} =Tr(\hat \rho\hat a)$ is given by the formula $_{\hat \rho}= \int \limits_{0}^{2\pi}\int \limits_{-\infty}^{+\infty}w_{\hat \rho}(X,\phi)a(X,\phi)dXd\phi$. The class $\mathcal A$ includes all the symmetrized polynomials of canonical variables $\hat q$ and $\hat p$.Comment: 8 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

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 $\theta$), the behavior for large and small distances is analyzed.Comment: 5 page

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