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We construct a `non-unital spectral triple of finite volume' out of the Moyal product and a differential square root of the harmonic oscillator Hamiltonian.
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V. Gayral, J. M. Gracia-Bondía, B. Iochum, T. Schücker and J. C. Várilly, “Moyal planes are spectral triples,” Commun. Math. Phys. 246
2004
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H. Grosse and R. Wulkenhaar, “The beta-function in duality-covariant noncommutative ϕ 4 \phi^{4} -theory,” Eur. Phys. J. C 35
2004
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V. Gayral and B. Iochum, “The spectral action for Moyal planes,” J. Math. Phys. 46
2005
Cited alongside, same era.
H. Grosse and R. Wulkenhaar, “Power-counting theorem for non-local matrix models and renormalisation,” Commun. Math. Phys. 254
2005
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H. Grosse and R. Wulkenhaar, “Renormalisation of ϕ 4 \phi^{4} -theory on noncommutative ℝ 4 \mathbb{R}^{4} in the matrix base,” Commun. Math. Phys. 256
2005
Cited alongside, same era.
H. Grosse and R. Wulkenhaar, “Renormalisation of ϕ 4 \phi^{4} -theory on non-commutative ℝ 4 \mathbb{R}^{4} to all orders,” Lett. Math. Phys. 71
2005
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A. H. Chamseddine and A. Connes, “Scale invariance in the spectral action,” J. Math. Phys. 47
2006
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M. Disertori, R. Gurau, J. Magnen and V. Rivasseau, “Vanishing of beta function of noncommutative ϕ 4 4 \phi^{4}_{4} theory to all orders,” Phys. Lett. B 649
2007
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A. de Goursac, J. C. Wallet and R. Wulkenhaar, “Noncommutative induced gauge theory,” Eur. Phys. J. C 51
2007
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H. Grosse and M. Wohlgenannt, “Induced Gauge Theory on a Noncommutative Space,” Eur. Phys. J. C 52
2007
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R. Gurau and V. Rivasseau, “Parametric representation of noncommutative field theory,” Commun. Math. Phys. 272
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V. Rivasseau, “Constructive Matrix Theory,” J. High Energy Phys. 9
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A. Connes, “Noncommutative geometry and the standard model with neutrino mixing,” JHEP 0611
2006
Cited alongside, same era.
R. Gurau, J. Magnen, V. Rivasseau and F. Vignes-Tourneret, “Renormalization of non-commutative ϕ 4 4 \phi^{4}_{4} field theory in x x -space,” Commun. Math. Phys. 267
2006
Cited alongside, same era.
V. Rivasseau, F. Vignes-Tourneret and R. Wulkenhaar, “Renormalization of noncommutative ϕ 4 \phi^{4} -theory by multi-scale analysis,” Commun. Math. Phys. 262
2006
Cited alongside, same era.
M. Disertori and V. Rivasseau, “Two and three loops beta function of noncommutative ϕ 4 4 \phi^{4}_{4} theory,” Eur. Phys. J. C 50
2007
Cited alongside, same era.
A. Carey, V. Gayral, A. Rennie and F. Sukochev, “Integration on locally compact noncommutative spaces,” [arXiv:math.OA/0912.2817]
Cited in the paper.
A. Carey, V. Gayral, A. Rennie and F. Sukochev, “Index theory for locally compact noncommutative geometries,” [arXiv:math.OA/1107.0805]
Cited in the paper.
H. Grosse and R. Wulkenhaar, “8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory,” [arXiv:hep-th/0709.0095]
Cited in the paper.
2007
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J. Magnen and V. Rivasseau, “Constructive ϕ 4 \phi^{4} field theory without tears,” Ann. Henri Poincaré 9
2008
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R. Wulkenhaar, “Non-compact spectral triples with finite volume,” in Quanta of Maths
2010
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A. Connes, “On the spectral characterization of manifolds,” [arXiv:math.OA/0810.2088]
2088
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