On finite 4D quantum field theory in non-commutative geometry

Grosse, Harald; Klimčı́k, Ctirad; Prešnajder, P.

doi:10.1007/bf02099720

Cited by 168 publications

(253 citation statements)

References 15 publications

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“…Finally we note that it is possible and interesting to extend this kind of analysis to the noncommutative versions of these spaces utilising the framework of [9,10,11].…”

Section: Summary and Commentsmentioning

confidence: 99%

Quantum Hall effect in higher dimensions

2002

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Following recent work on the quantum Hall effect on S 4 , we solve the Landau problem on the complex projective spaces CP k and discuss quantum Hall states for such spaces. Unlike the case of S 4 , a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of CP 2 in some detail considering both Abelian and nonabelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of CP 3 is related to the case of S 4 .

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“…Finally we note that it is possible and interesting to extend this kind of analysis to the noncommutative versions of these spaces utilising the framework of [9,10,11].…”

Section: Summary and Commentsmentioning

confidence: 99%

Quantum Hall effect in higher dimensions

2002

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“…Much research has already gone into understanding noncommutative quantum field theory [12,13,14,15]; it is equivalent to working with ordinary (commutative) field theory and replacing the usual product by the ⋆ product defined as follows:…”

Section: Introductionmentioning

confidence: 99%

CPviolation from noncommutative geometry

Hinchliffe

Kersting

2001

Phys. Rev. D

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If the geometry of space-time is noncommutative, i.e. [x µ , x ν ] = iθ µν , then noncommutative CP violating effects may be manifest at low energies. For a noncommutative scale Λ ≡ θ −1/2 ≤ 2 T eV , CP violation from noncommutative geometry is comparable to that from the Standard Model (SM) alone: the noncommutative contributions to ǫ and ǫ ′ /ǫ in the Ksystem, may actually dominate over the Standard Model contributions. Present data permit noncommutative geometry to be the only source of CP violation. Furthermore the most recent findings for g − 2 of the muon are consistent with predictions from noncommutative geometry.

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“…Similarly using the explicit value of c 3 given in Section 4.1, one can also determine β n . Alternatively, they be calculated using creation -and annihilation operator techniques of [24], [23].…”

Section: Fuzzymentioning

confidence: 99%