876 research outputs found
Noncommutative Gravity and the *-Lie algebra of diffeomorphisms
We construct functions and tensors on noncommutative spacetime by
systematically twisting the corresponding commutative structures. The study of
the deformed diffeomorphisms (and Poincare) Lie algebra allows to construct a
noncomutative theory of gravity.Comment: 12 pages. Presented at the Erice International School of Subnuclear
Physics, 44th course, Erice, Sicily, 29.8- 7.9 2006, and at the Second
workshop and midterm meeting of the MCRTN ``Constituents, Fundamental Forces
and Symmetries of the Universe" Napoli, 9-13.10 200
Noncommutative gravity at second order via Seiberg-Witten map
We develop a general strategy to express noncommutative actions in terms of
commutative ones by using a recently developed geometric generalization of the
Seiberg-Witten map (SW map) between noncommutative and commutative fields.
We apply this general scheme to the noncommutative vierbein gravity action
and provide a SW differential equation for the action itself as well as a
recursive solution at all orders in the noncommutativity parameter \theta. We
thus express the action at order \theta^n+2 in terms of noncommutative fields
of order at most \theta^n+1 and, iterating the procedure, in terms of
noncommutative fields of order at most \theta^n.
This in particular provides the explicit expression of the action at order
\theta^2 in terms of the usual commutative spin connection and vierbein fields.
The result is an extended gravity action on commutative spacetime that is
manifestly invariant under local Lorentz rotations and general coordinate
transformations.Comment: 14 page
Proof of a Symmetrized Trace Conjecture for the Abelian Born-Infeld Lagrangian
In this paper we prove a conjecture regarding the form of the Born-Infeld
Lagrangian with a U(1)^2n gauge group after the elimination of the auxiliary
fields. We show that the Lagrangian can be written as a symmetrized trace of
Lorentz invariant bilinears in the field strength. More generally we prove a
theorem regarding certain solutions of unilateral matrix equations of arbitrary
order. For solutions which have perturbative expansions in the matrix
coefficients, the solution and all its positive powers are sums of terms which
are symmetrized in all the matrix coefficients and of terms which are
commutators.Comment: 9 pages, LaTeX, no figures, theorem generalized and a new method of
proof include
Strong Normalization for HA + EM1 by Non-Deterministic Choice
We study the strong normalization of a new Curry-Howard correspondence for HA
+ EM1, constructive Heyting Arithmetic with the excluded middle on
Sigma01-formulas. The proof-term language of HA + EM1 consists in the lambda
calculus plus an operator ||_a which represents, from the viewpoint of
programming, an exception operator with a delimited scope, and from the
viewpoint of logic, a restricted version of the excluded middle. We give a
strong normalization proof for the system based on a technique of
"non-deterministic immersion".Comment: In Proceedings COS 2013, arXiv:1309.092
On the Geometry of the Quantum Poincare Group
We review the construction of the multiparametric inhomogeneous orthogonal
quantum group ISO_qr(N) as a projection from SO_qr(N+2), and recall the
conjugation that for N=4 leads to the quantum Poincare group. We study the
properties of the universal enveloping algebra U_qr(iso(N)), and give an
R-matrix formulation. A quantum Lie algebra and a bicovariant differential
calculus on twisted ISO(N) are found.Comment: 12 pages, Latex. Contribution to the proceedings of the 30-th
Arhenshoop Symposium on the Theory of Elementary Particles. August 1996. To
appear in Nucl. Phys. B Proc. Sup
Real forms of quantum orthogonal groups, q-Lorentz groups in any dimension
We review known real forms of the quantum orthogonal groups SO_q(N). New
*-conjugations are then introduced and we contruct all real forms of quantum
orthogonal groups. We thus give an RTT formulation of the *-conjugations on
SO_q(N) that is complementary to the U_q(g) *-structure classification of
Twietmeyer \cite{Twietmeyer}. In particular we easily find and describe the
real forms SO_q(N-1,1) for any value of N. Quantum subspaces of the q-Minkowski
space are analized.Comment: Latex, 13 pages. Added ref. [4] and [7] (page 12
Deformation quantization of principal bundles
We outline how Drinfeld twist deformation techniques can be applied to the
deformation quantization of principal bundles into noncommutative principal
bundles, and more in general to the deformation of Hopf-Galois extensions.
First we twist deform the structure group in a quantum group, and this leads to
a deformation of the fibers of the principal bundle. Next we twist deform a
subgroup of the group of authomorphisms of the principal bundle, and this leads
to a noncommutative base space. Considering both deformations we obtain
noncommutative principal bundles with noncommutative fiber and base space as
well.Comment: 20 pages. Contribution to the volume in memory of Professor Mauro
Francaviglia. Based on joint work with Pierre Bieliavsky, Chiara Pagani and
Alexander Schenke
Twisting all the way: from algebras to morphisms and connections
Given a Hopf algebra H and an algebra A that is an H-module algebra we
consider the category of left H-modules and A-bimodules, where morphisms are
just right A-linear maps (not necessarily H-equivariant). Given a twist F of H
we then quantize (deform) H to H^F, A to A_\star and correspondingly the
category of left H-modules and A-bimodules to the category of left H^F-modules
and A_\star-bimodules. If we consider a quasitriangular Hopf algebra H, a
quasi-commutative algebra A and quasi-commutative A-bimodules, we can further
construct and study tensor products over A of modules and of morphisms, and
their twist quantization.
This study leads to the definition of arbitrary (i.e., not necessarily
H-equivariant) connections on quasi-commutative A-bimodules, to extend these
connections to tensor product modules and to quantize them to A_\star-bimodule
connections. Their curvatures and those on tensor product modules are also
determined.Comment: 15 pages. Proceedings of the Julius Wess 2001 workshop of the Balkan
Summer Institute 2011, 27-28.8.2011 Donji Milanovac, Serbi
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