998 research outputs found
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.
Lorentz-covariant deformed algebra with minimal length
The -dimensional two-parameter deformed algebra with minimal length
introduced by Kempf is generalized to a Lorentz-covariant algebra describing a
()-dimensional quantized space-time. For D=3, it includes Snyder algebra
as a special case. The deformed Poincar\'e transformations leaving the algebra
invariant are identified. Uncertainty relations are studied. In the case of D=1
and one nonvanishing parameter, the bound-state energy spectrum and
wavefunctions of the Dirac oscillator are exactly obtained.Comment: 8 pages, no figure, presented at XV International Colloquium on
Integrable Systems and Quantum Symmetries (ISQS-15), Prague, June 15-17, 200
Kontsevich product and gauge invariance
We analyze the question of gauge invariance in a flat
non-commutative space where the parameter of non-commutativity,
, is a local function satisfying Jacobi identity (and
thereby leading to an associative Kontsevich product). We show that in this
case, both gauge transformations as well as the definitions of covariant
derivatives have to modify so as to have a gauge invariant action. We work out
the gauge invariant actions for the matter fields in the fundamental and the
adjoint representations up to order while we discuss the gauge
invariant Maxwell theory up to order . We show that despite the
modifications in the gauge transformations, the covariant derivative and the
field strength, Seiberg-Witten map continues to hold for this theory. In this
theory, translations do not form a subgroup of the gauge transformations
(unlike in the case when is a constant) which is reflected in
the stress tensor not being conserved.Comment: 7 page
Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
We describe the deformed Poincare-conformal symmetries implying the
covariance of the noncommutative space obeying Snyder's algebra. Relativistic
particle models invariant under these deformed symmetries are presented. A
gauge (reparametrisation) independent derivation of
Snyder's algebra from such models is given. The algebraic transformations
relating the deformed symmetries with the usual (undeformed) ones are provided.
Finally, an alternative form of an action yielding Snyder's algebra is
discussed where the mass of a relativistic particle gets identified with the
inverse of the noncommutativity parameter.Comment: 19 pages; Latex; title changed, 3 new references added and minor
changes; to appear in JHE
Differential calculus and gauge transformations on a deformed space
Deformed gauge transformations on deformed coordinate spaces are considered
for any Lie algebra. The representation theory of this gauge group forces us to
work in a deformed Lie algebra as well. This deformation rests on a twisted
Hopf algebra, thus we can represent a twisted Hopf algebra on deformed spaces.
That leads to the construction of Lagrangian invariant under a twisted Lie
algebra.Comment: 14 pages, to appear in General Relativity and Gravitation Journal,
Obregon's Festschrift 2006, V2: misprints correcte
Probing Noncommutative Space-Time in the Laboratory Frame
The phenomenological investigation of noncommutative space-time in the
laboratory frame are presented. We formulate the apparent time variation of
noncommutativity parameter in the laboratory frame due to the
earth's rotation. Furthermore, in the noncommutative QED, we discuss how to
probe the electric-like component
by the
process at future linear collider.
We may determine the magnitude and the direction of
by detailed study of the apparent time
variation of total cross section.
In case of us observing no signal, the upper limit on the magnitude of
can be determined independently of its
direction.Comment: 12 pages, 7 figures, typos are corrected, one graph have been added
in figure
Noncommutative Geometry as a Regulator
We give a perturbative quantization of space-time in the case where the
commutators of the underlying algebra
generators are not central . We argue that this kind of quantum space-times can
be used as regulators for quantum field theories . In particular we show in the
case of the theory that by choosing appropriately the commutators
we can remove all the infinities by reproducing all the
counter terms . In other words the renormalized action on plus the
counter terms can be rewritten as only a renormalized action on the quantum
space-time . We conjecture therefore that renormalization of quantum
field theory is equivalent to the quantization of the underlying space-time
.Comment: Latex, 30 pages, no figures,typos corrected,references added .
Substantial amount of rewriting of the last section . Final interesting
remarks added at the end of the pape
Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory
A \star-product is defined via a set of commuting vector fields X_a = e_a^\mu
(x) \partial_\mu, and used in a phi^*4 theory coupled to the e_a^\mu (x)
fields. The \star-product is dynamical, and the vacuum solution phi =0, e_a^\mu
(x)=delta_a^\mu reproduces the usual Moyal product. The action is invariant
under rigid translations and Lorentz rotations, and the conserved
energy-momentum and angular momentum tensors are explicitly derived.Comment: 15 pages LaTeX, minor typos, added reference
DFR Perturbative Quantum Field theory on Quantum Space Time, and Wick Reduction
We discuss the perturbative approach a` la Dyson to a quantum field theory
with nonlocal self-interaction :phi*...*phi:, according to Doplicher,
Fredenhagen and Roberts (DFR). In particular, we show that the Wick reduction
of non locally time--ordered products of Wick monomials can be performed as
usual, and we discuss a very simple Dyson diagram.Comment: 15 pages, pdf has active hyperlinks. To appear in the proceedings of
the conference on "Rigorous quantum Field Theory", held at Saclay on July
19-21, 2004, on the occasion of Jacques Bros' 70th birthda
The Hamiltonian BRST quantization of a noncommutative nonabelian gauge theory and its Seiberg-Witten map
We consider the Hamiltonian BRST quantization of a noncommutative non abelian
gauge theory. The Seiberg-Witten map of all phase-space variables, including
multipliers, ghosts and their momenta, is given in first order in the
noncommutative parameter . We show that there exists a complete
consistence between the gauge structures of the original and of the mapped
theories, derived in a canonical way, once we appropriately choose the map
solutions.Comment: 10 pages, Latex. Address adde
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