110 research outputs found
Nambu-Poisson Gauge Theory
We generalize noncommutative gauge theory using Nambu-Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg-Witten map. We construct a covariant Nambu-Poisson gauge theory action, give its first order expansion in the Nambu-Poisson tensor and relate it to a Nambu-Poisson matrix model
Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map
We use the Seiberg-Witten map (SW map) to expand noncommutative gravity
coupled to fermions in terms of ordinary commuting fields. The action is
invariant under general coordinate transformations and local Lorentz rotations,
and has the same degrees of freedom as the commutative gravity action. The
expansion is given up to second order in the noncommutativity parameter
{\theta}. A geometric reformulation and generalization of the SW map is
presented that applies to any abelian twist. Compatibility of the map with
hermiticity and charge conjugation conditions is proven. The action is shown to
be real and invariant under charge conjugation at all orders in {\theta}. This
implies the bosonic part of the action to be even in {\theta}, while the
fermionic part is even in {\theta} for Majorana fermions.Comment: 27 pages, LaTeX. Revised version with proof of charge conjugation
symmetry of the NC action and its parity under theta --> - theta (see new
sect. 2.6, sect. 6 and app. B). References added. arXiv admin note:
substantial text overlap with arXiv:0902.381
A C*-Algebraic Model for Locally Noncommutative Spacetimes
Locally noncommutative spacetimes provide a refined notion of noncommutative
spacetimes where the noncommutativity is present only for small distances. Here
we discuss a non-perturbative approach based on Rieffel's strict deformation
quantization. To this end, we extend the usual C*-algebraic results to a
pro-C*-algebraic framework.Comment: 13 pages, LaTeX 2e, no figure
Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)]
There being no precise definition of the quantum integrability, the
separability of variables can serve as its practical substitute. For any
quantum integrable model generated by the Yangian Y[sl(3)] the canonical
coordinates and the conjugated operators are constructed which satisfy the
``quantum characteristic equation'' (quantum counterpart of the spectral
algebraic curve for the L operator). The coordinates constructed provide a
local separation of variables. The conditions are enlisted which are necessary
for the global separation of variables to take place.Comment: 15 page
Coherent states for Hopf algebras
Families of Perelomov coherent states are defined axiomatically in the
context of unitary representations of Hopf algebras possessing a Haar integral.
A global geometric picture involving locally trivial noncommutative fibre
bundles is involved in the construction. A noncommutative resolution of
identity formula is proved in that setup. Examples come from quantum groups.Comment: 19 pages, uses kluwer.cls; the exposition much improved; an example
of deriving the resolution of identity via coherent states for SUq(2) added;
the result differs from the proposals in literatur
The Standard Model on Non-Commutative Space-Time: Electroweak Currents and Higgs Sector
In this article we review the electroweak charged and neutral currents in the
Non-Commutative Standard Model (NCSM) and compute the Higgs and Yukawa parts of
the NCSM action. With the aim to make the NCSM accessible to phenomenological
considerations, all relevant expressions are given in terms of physical fields
and Feynman rules are provided.Comment: 33 pages, axodraw.sty; shortened, comments and references added,
version to appear in EPJ
Possible Effects of Noncommutative Geometry on Weak CP Violation and Unitarity Triangles
Possible effects of noncommutative geometry on weak CP violation and
unitarity triangles are discussed by taking account of a simple version of the
momentum-dependent quark mixing matrix in the noncommutative standard model. In
particular, we calculate nine rephasing invariants of CP violation and
illustrate the noncommutative CP-violating effect in a couple of charged
D-meson decays. We also show how inner angles of the deformed unitarity
triangles are related to CP-violating asymmetries in some typical B_d and B_s
transitions into CP eigenstates. B-meson factories are expected to help probe
or constrain noncommutative geometry at low energies in the near future.Comment: RexTev 16 pages. Modifications made. References added. Accepted for
publication in Phys. Rev.
Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
We develop quantization techniques for describing the nonassociative geometry
probed by closed strings in flat non-geometric R-flux backgrounds M. Starting
from a suitable Courant sigma-model on an open membrane with target space M,
regarded as a topological sector of closed string dynamics in R-space, we
derive a twisted Poisson sigma-model on the boundary of the membrane whose
target space is the cotangent bundle T^*M and whose quasi-Poisson structure
coincides with those previously proposed. We argue that from the membrane
perspective the path integral over multivalued closed string fields in Q-space
is equivalent to integrating over open strings in R-space. The corresponding
boundary correlation functions reproduce Kontsevich's deformation quantization
formula for the twisted Poisson manifolds. For constant R-flux, we derive
closed formulas for the corresponding nonassociative star product and its
associator, and compare them with previous proposals for a 3-product of fields
on R-space. We develop various versions of the Seiberg-Witten map which relate
our nonassociative star products to associative ones and add fluctuations to
the R-flux background. We show that the Kontsevich formula coincides with the
star product obtained by quantizing the dual of a Lie 2-algebra via convolution
in an integrating Lie 2-group associated to the T-dual doubled geometry, and
hence clarify the relation to the twisted convolution products for topological
nonassociative torus bundles. We further demonstrate how our approach leads to
a consistent quantization of Nambu-Poisson 3-brackets.Comment: 52 pages; v2: references adde
Morita Equivalence, Picard Groupoids and Noncommutative Field Theories
In this article we review recent developments on Morita equivalence of star
products and their Picard groups. We point out the relations between
noncommutative field theories and deformed vector bundles which give the Morita
equivalence bimodules.Comment: Latex2e, 10 pages. Conference Proceeding for the Sendai Meeting 2002.
Some typos fixe
More on quantum groups from the the quantization point of view
Star products on the classical double group of a simple Lie group and on
corresponding symplectic grupoids are given so that the quantum double and the
"quantized tangent bundle" are obtained in the deformation description.
"Complex" quantum groups and bicovariant quantum Lie algebras are discused from
this point of view. Further we discuss the quantization of the Poisson
structure on symmetric algebra leading to the quantized enveloping
algebra as an example of biquantization in the sense of Turaev.
Description of in terms of the generators of the bicovariant
differential calculus on is very convenient for this purpose. Finally
we interpret in the deformation framework some well known properties of compact
quantum groups as simple consequences of corresponding properties of classical
compact Lie groups. An analogue of the classical Kirillov's universal character
formula is given for the unitary irreducible representation in the compact
case.Comment: 18 page
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