Renormalisation of φ^4-theory on noncommutative R^4 in the matrix base

Details Renormalisation of φ^4-theory on noncommutative R^4 in the matrix base Renormalisation of φ^4-theory on noncommutative R^4 in the matrix base

2004-01-20

arxiv.org/abs/hep-th/0401128v2

Commun.Math.Phys.256:305-374,2005

Physics

High Energy Physics

High Energy Physics - Theory

64 pages, 63 figures, LaTeX with svjour macros. v2: section on the strategy of the proof added, integration procedure improved

Scientific paper

10.1007/s00220-004-1285-2

We prove that the real four-dimensional Euclidean noncommutative \phi^4-model is renormalisable to all orders in perturbation theory. Compared with the commutative case, the bare action of relevant and marginal couplings contains necessarily an additional term: an harmonic oscillator potential for the free scalar field action. This entails a modified dispersion relation for the free theory, which becomes important at large distances (UV/IR-entanglement). The renormalisation proof relies on flow equations for the expansion coefficients of the effective action with respect to scalar fields written in the matrix base of the noncommutative R^4. The renormalisation flow depends on the topology of ribbon graphs and on the asymptotic and local behaviour of the propagator governed by orthogonal Meixner polynomials.

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