Noncommutative Scalar Field Coupled to Gravity

A model for a noncommutative scalar field coupled to gravity is proposed via an extension of the Moyal product. It is shown that there are solutions compatible with homogeneity and isotropy to first non-trivial order in the perturbation of the star-product, with the gravity sector described by a flat Robertson-Walker metric. We show that in the slow-roll regime of a typical chaotic inflationary scenario, noncommutativity has negligible impact.Comment: Revtex4, 6 pages. Final version to appear at Phys. Rev.

Angles in Fuzzy Disc and Angular Noncommutative Solitons

The fuzzy disc, introduced by the authors of Ref.[1], is a disc-shaped region in a noncommutative plane, and is a fuzzy approximation of a commutative disc. In this paper we show that one can introduce a concept of angles to the fuzzy disc, by using the phase operator and phase states known in quantum optics. We gave a description of a fuzzy disc in terms of operators and their commutation relations, and studied properties of angular projection operators. A similar construction for a fuzzy annulus is also given. As an application, we constructed fan-shaped soliton solutions of a scalar field theory on a fuzzy disc, which corresponds to a fan-shaped D-brane. We also applied this concept to the theory of noncommutative gravity that we proposed in Ref.[2]. In addition, possible connections to black hole microstates, holography and an experimental test of noncommutativity by laser physics are suggested.Comment: 24 pages, 12 figures; v2: minor mistake corrected in Eq.(3.21), and discussion adapted accordingly; v3: a further discussion on the algebra of the fuzzy disc added in subsection 3.2; v4: discussions improved and typos correcte

Confinement in Gauge Theories from the Condensation of World-Sheet Defects in Liouville String

We present a Liouville-string approach to confinement in four-dimensional gauge theories, which extends previous approaches to include non-conformal theories. We consider Liouville field theory on world sheets whose boundaries are the Wilson loops of gauge theory, which exhibit vortex and spike defects. We show that world-sheet vortex condensation occurs when the Wilson loop is embedded in four target space-time dimensions, and show that this corresponds to the condensation of gauge magnetic monopoles in target space. We also show that vortex condensation generates a effective string tension corresponding to the confinement of electric degrees of freedom. The tension is independent of the string length in a gauge theory whose electric coupling varies logarithmically with the length scale. The Liouville field is naturally interpreted as an extra target dimension, with an anti-de-Sitter (AdS) structure induced by recoil effects on the gauge monopoles, interpreted as D branes of the effective string theory. Black holes in the bulk AdS space correspond to world-sheet defects, so that phases of the bulk gravitational system correspond to the different world-sheet phases, and hence to different phases of the four-dimensional gauge theory. Deconfinement is associated with a Berezinskii-Kosterlitz-Thouless transition of vortices on the Wilson-loop world sheet, corresponding in turn to a phase transition of the black holes in the bulk AdS space.Comment: 29 pages LATEX, three eps figures incorporate

Quantum Field Theory on the Noncommutative Plane with Eq(2)E_q(2) Symmetry

We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we define quantum fields depending on noncommutative coordinates and construct a field theoretical action using the $E_q(2)$-invariant measure on the noncommutative plane. With the help of the partial wave decomposition we show that this quantum field theory can be considered as a second quantization of the particle theory on the noncommutative plane and that this field theory has (contrary to the common belief) even more severe ultraviolet divergences than its counterpart on the usual commutative plane. Finally, we introduce the symmetry transformations of physical states on noncommutative spaces and discuss them in detail for the case of the $E_q(2)$ quantum group.Comment: LaTeX, 26 page

Observational constraints on patch inflation in noncommutative spacetime

We study constraints on a number of patch inflationary models in noncommutative spacetime using a compilation of recent high-precision observational data. In particular, the four-dimensional General Relativistic (GR) case, the Randall-Sundrum (RS) and Gauss-Bonnet (GB) braneworld scenarios are investigated by extending previous commutative analyses to the infrared limit of a maximally symmetric realization of the stringy uncertainty principle. The effect of spacetime noncommutativity modifies the standard consistency relation between the tensor spectral index and the tensor-to-scalar ratio. We perform likelihood analyses in terms of inflationary observables using new consistency relations and confront them with large-field inflationary models with potential V \propto \vp^p in two classes of noncommutative scenarios. We find a number of interesting results: (i) the quartic potential (p=4) is rescued from marginal rejection in the class 2 GR case, and (ii) steep inflation driven by an exponential potential (p \to \infty) is allowed in the class 1 RS case. Spacetime noncommutativity can lead to blue-tilted scalar and tensor spectra even for monomial potentials, thus opening up a possibility to explain the loss of power observed in the cosmic microwave background anisotropies. We also explore patch inflation with a Dirac-Born-Infeld tachyon field and explicitly show that the associated likelihood analysis is equivalent to the one in the ordinary scalar field case by using horizon-flow parameters. It turns out that tachyon inflation is compatible with observations in all patch cosmologies even for large p.Comment: 16 pages, 11 figures; v2: updated references, minor corrections to match the Phys. Rev. D versio

String Tension and the Generation of the Conformal Anomaly

The origin of the string conformal anomaly is studied in detail. We use a reformulated string Lagrangian which allows to consider the string tension $T_{0}$ as a small perturbation. The expansion parameter is the worldsheet speed of light c, which is proportional to $T_{0}$ . We examine carefully the interplay between a null (tensionless) string and a tensionful string which includes orders $c^{2}$ and higher. The conformal algebra generated by the constraints is considered. At the quantum level the normal ordering provides a central charge proportional to $c^{2}$. Thus it is clear that quantum null strings respect conformal invariance and it is the string tension which generates the conformal anomaly.Comment: More references are included. Final version, to appear in Phys.Rev.D. 6 pages, LaTex, no figure

American Institute of Ultrasound in Medicine

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24836/1/0000262.pd

About maximally localized states in quantum mechanics

We analyze the emergence of a minimal length for a large class of generalized commutation relations, preserving commutation of the position operators and translation invariance as well as rotation invariance (in dimension higher than one). We show that the construction of the maximally localized states based on squeezed states generally fails. Rather, one must resort to a constrained variational principle.Comment: accepted for publication in PR

Nonpointlike Particles in Harmonic Oscillators

Quantum mechanics ordinarily describes particles as being pointlike, in the sense that the uncertainty $\Delta x$ can, in principle, be made arbitrarily small. It has been shown that suitable correction terms to the canonical commutation relations induce a finite lower bound to spatial localisation. Here, we perturbatively calculate the corrections to the energy levels of an in this sense nonpointlike particle in isotropic harmonic oscillators. Apart from a special case the degeneracy of the energy levels is removed.Comment: LaTeX, 9 pages, 1 figure included via epsf optio