A remark on polar noncommutativity
Noncommutative space has been found to be of use in a number of different contexts. In particular, one may use noncommutative spacetime to generate quantised gravity theories. Via an identification between the Moyal ⋆-product on function space and commutators on a Hilbert space, one may use the Seib...
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2015-06-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269315003068 |
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doaj-3f8c4593f47c446f9791ec2bc8a005182020-11-24T23:11:22ZengElsevierPhysics Letters B0370-26932015-06-017462527A remark on polar noncommutativityAndrew Iskauskas0Department of Mathematical Sciences, Durham University, Lower Mountjoy, Stockton Road, Durham DH1 3LE, UKNoncommutative space has been found to be of use in a number of different contexts. In particular, one may use noncommutative spacetime to generate quantised gravity theories. Via an identification between the Moyal ⋆-product on function space and commutators on a Hilbert space, one may use the Seiberg–Witten map to generate corrections to such gravity theories. However, care must be taken with the derivation of commutation relations. We examine conditions for the validity of such an approach, and motivate the correct form for polar noncommutativity in R2. Such an approach lends itself readily to extension to more complicated spacetime parametrisations. Keywords: Noncommutativity, Polar coordinates, Seiberg–Wittenhttp://www.sciencedirect.com/science/article/pii/S0370269315003068 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Andrew Iskauskas |
| spellingShingle |
Andrew Iskauskas A remark on polar noncommutativity Physics Letters B |
| author_facet |
Andrew Iskauskas |
| author_sort |
Andrew Iskauskas |
| title |
A remark on polar noncommutativity |
| title_short |
A remark on polar noncommutativity |
| title_full |
A remark on polar noncommutativity |
| title_fullStr |
A remark on polar noncommutativity |
| title_full_unstemmed |
A remark on polar noncommutativity |
| title_sort |
remark on polar noncommutativity |
| publisher |
Elsevier |
| series |
Physics Letters B |
| issn |
0370-2693 |
| publishDate |
2015-06-01 |
| description |
Noncommutative space has been found to be of use in a number of different contexts. In particular, one may use noncommutative spacetime to generate quantised gravity theories. Via an identification between the Moyal ⋆-product on function space and commutators on a Hilbert space, one may use the Seiberg–Witten map to generate corrections to such gravity theories. However, care must be taken with the derivation of commutation relations. We examine conditions for the validity of such an approach, and motivate the correct form for polar noncommutativity in R2. Such an approach lends itself readily to extension to more complicated spacetime parametrisations. Keywords: Noncommutativity, Polar coordinates, Seiberg–Witten |
| url |
http://www.sciencedirect.com/science/article/pii/S0370269315003068 |
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AT andrewiskauskas aremarkonpolarnoncommutativity AT andrewiskauskas remarkonpolarnoncommutativity |
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