240 research outputs found
Gauge Theory of the Star Product
The choice of a star product realization for noncommutative field theory can
be regarded as a gauge choice in the space of all equivalent star products.
With the goal of having a gauge invariant treatment, we develop tools, such as
integration measures and covariant derivatives on this space. The covariant
derivative can be expressed in terms of connections in the usual way giving
rise to new degrees of freedom for noncommutative theories.Comment: 16 page
Elementary Derivation of the Chiral Anomaly
An elementary derivation of the chiral gauge anomaly in all even dimensions
is given in terms of noncommutative traces of pseudo-differential operators.Comment: Minor errors and misprints corrected, a reference added. AmsTex file,
12 output pages. If you do not have preloaded AmsTex you have to \input
amstex.te
String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy
We consider scalar-Gauss-Bonnet and modified Gauss-Bonnet gravities and
reconstruct these theories from the universe expansion history. In particular,
we are able to construct versions of those theories (with and without ordinary
matter), in which the matter dominated era makes a transition to the cosmic
acceleration epoch. It is remarkable that, in several of the cases under
consideration, matter dominance and the deceleration-acceleration transition
occur in the presence of matter only. The late-time acceleration epoch is
described asymptotically by de Sitter space but may also correspond to an exact
CDM cosmology, having in both cases an effective equation of state
parameter close to -1. The one-loop effective action of modified
Gauss-Bonnet gravity on the de Sitter background is evaluated and it is used to
derive stability criteria for the ensuing de Sitter universe.Comment: LaTeX20 pages, 4 figures, version to apear in PR
Noncommutative geometry and lower dimensional volumes in Riemannian geometry
In this paper we explain how to define "lower dimensional'' volumes of any
compact Riemannian manifold as the integrals of local Riemannian invariants.
For instance we give sense to the area and the length of such a manifold in any
dimension. Our reasoning is motivated by an idea of Connes and involves in an
essential way noncommutative geometry and the analysis of Dirac operators on
spin manifolds. However, the ultimate definitions of the lower dimensional
volumes don't involve noncommutative geometry or spin structures at all.Comment: 12 page
Curvature in Noncommutative Geometry
Our understanding of the notion of curvature in a noncommutative setting has
progressed substantially in the past ten years. This new episode in
noncommutative geometry started when a Gauss-Bonnet theorem was proved by
Connes and Tretkoff for a curved noncommutative two torus. Ideas from spectral
geometry and heat kernel asymptotic expansions suggest a general way of
defining local curvature invariants for noncommutative Riemannian type spaces
where the metric structure is encoded by a Dirac type operator. To carry
explicit computations however one needs quite intriguing new ideas. We give an
account of the most recent developments on the notion of curvature in
noncommutative geometry in this paper.Comment: 76 pages, 8 figures, final version, one section on open problems
added, and references expanded. Appears in "Advances in Noncommutative
Geometry - on the occasion of Alain Connes' 70th birthday
Classical and quantum ergodicity on orbifolds
We extend to orbifolds classical results on quantum ergodicity due to
Shnirelman, Colin de Verdi\`ere and Zelditch, proving that, for any positive,
first-order self-adjoint elliptic pseudodifferential operator P on a compact
orbifold X with positive principal symbol p, ergodicity of the Hamiltonian flow
of p implies quantum ergodicity for the operator P. We also prove ergodicity of
the geodesic flow on a compact Riemannian orbifold of negative sectional
curvature.Comment: 14 page
Muon capture on light nuclei
This work investigates the muon capture reactions 2H(\mu^-,\nu_\mu)nn and
3He(\mu^-,\nu_\mu)3H and the contribution to their total capture rates arising
from the axial two-body currents obtained imposing the
partially-conserved-axial-current (PCAC) hypothesis. The initial and final A=2
and 3 nuclear wave functions are obtained from the Argonne v_{18} two-nucleon
potential, in combination with the Urbana IX three-nucleon potential in the
case of A=3. The weak current consists of vector and axial components derived
in chiral effective field theory. The low-energy constant entering the vector
(axial) component is determined by reproducting the isovector combination of
the trinucleon magnetic moment (Gamow-Teller matrix element of tritium
beta-decay). The total capture rates are 393.1(8) s^{-1} for A=2 and 1488(9)
s^{-1} for A=3, where the uncertainties arise from the adopted fitting
procedure.Comment: 6 pages, submitted to Few-Body Sys
Interaction of Low - Energy Induced Gravity with Quantized Matter -- II. Temperature effects
At the very early Universe the matter fields are described by the GUT models
in curved space-time. At high energies these fields are asymptotically free and
conformally coupled to external metric. The only possible quantum effect is the
appearance of the conformal anomaly, which leads to the propagation of the new
degree of freedom - conformal factor. Simultaneously with the expansion of the
Universe, the scale of energies decreases and the propagating conformal factor
starts to interact with the Higgs field due to the violation of conformal
invariance in the matter fields sector. In a previous paper \cite{foo} we have
shown that this interaction can lead to special physical effects like the
renormalization group flow, which ends in some fixed point. Furthermore in the
vicinity of this fixed point there occur the first order phase transitions. In
the present paper we consider the same theory of conformal factor coupled to
Higgs field and incorporate the temperature effects. We reduce the complicated
higher-derivative operator to several ones of the standard second-derivative
form and calculate an exact effective potential with temperature on the anti de
Sitter (AdS) background.Comment: 12 pages, LaTex - 2 Figure
Noncommutative Induced Gauge Theory
We consider an external gauge potential minimally coupled to a renormalisable
scalar theory on 4-dimensional Moyal space and compute in position space the
one-loop Yang-Mills-type effective theory generated from the integration over
the scalar field. We find that the gauge invariant effective action involves,
beyond the expected noncommutative version of the pure Yang-Mills action,
additional terms that may be interpreted as the gauge theory counterpart of the
harmonic oscillator term, which for the noncommutative -theory on Moyal
space ensures renormalisability. The expression of a possible candidate for a
renormalisable action for a gauge theory defined on Moyal space is conjectured
and discussed.Comment: 20 pages, 6 figure
On the scalar curvature for the noncommutative four torus
The canonical flat metric of the noncommutative four torus is conformally perturbed and the term corresponding to the scalar curvature in the heat kernel expansion of perturbed Laplacian is calculated by using an analog of the Wodziski residue. This allows the calculation to be done without using the so called rearrangement lemma. Thus, because of the simplicity of the method, the structure of the one and two variable of functions of a modular automorphism that appear in the formula for the curvature can be understood and functional relations among them are discovered. Also the gradient of the analog of the Einstein-Hilbert action is calculated explicitly, which prepares the ground for defining certain geometric flows (such as the Yamabe flow) on the noncommutative four torus
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