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Ruíz Ruíz, Fernando and Gayral, V. and Gracia Bondía, Jose Mariano (2005) Positiondependent noncommutative products: classical construction and field theory. Nuclear Physics B, 727 (3). pp. 513536. ISSN 05503213
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Official URL: http://dx.doi.org/10.1016/j.nuclphysb.2005.08.016
URL  URL Type 

http://arxiv.org/abs/hepth/0504022  Organisation 
http://www.sciencedirect.com  Publisher 
Abstract
We look in Euclidean R4 for associative star products realizing the commutation relation [x(mu), x(upsilon)] i Theta(mu upsilon)(x), where the noncommutativity parameters Theta(mu upsilon) depend on the position coordinates x. We do this by adopting Rieffel's deformation theory (originally formulated for constant Theta and which includes the Moyal product as a particular case) and find that, for a topology R2 x R2, there is only one class of such products which are associative. It corresponds to a noncommutativity matrix whose canonical form has components Theta(12) = Theta(21) = 0 and Theta(34) = Theta(43) = theta(x(1), x(2)), with theta(x (1), x(2)) an arbitrary positive smooth bounded function. In Minkowski spacetime, this describes a positiondependent spacelike or magnetic noncommutativity. We show how to generalize our construction to n >= 3 arbitrary dimensions and use it to find traveling noncommutative lumps generalizing noncommutative solitons discussed in the literature. Next we consider Euclidean lambda phi(4) field theory on such a noncommutative background. Using a zetalike regulator, the covariant perturbation method and working in configuration space, we explicitly compute the UV singularities. We find that, while the twopoint UV divergences are nonlocal, the fourpoint UV divergences are local, in accordance with recent results for constant Ѳ.
Item Type:  Article 

Additional Information:  © 2005 Elsevier B.V. All rights reserved. 
Uncontrolled Keywords:  Space QuantumMechanics, Manifolds, Time, Deformations, Unitarity, Algebras 
Subjects:  Sciences > Physics 
ID Code:  24948 
Deposited On:  07 Apr 2014 16:09 
Last Modified:  07 Apr 2014 16:09 
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