Renormalisation of \phi^4-theory on noncommutative R^4 in the matrix base
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/0401128,
title = {Renormalisation of \phi^4-theory on noncommutative R^4 in the matrix base},
author = {Harald Grosse and Raimar Wulkenhaar},
journal= {arXiv preprint arXiv:hep-th/0401128},
year = {2008}
}
Comments
64 pages, 63 figures, LaTeX with svjour macros. v2: section on the strategy of the proof added, integration procedure improved so that the initial cut-off can be directly removed, conclusion extended, many typos corrected; to appear in Commun. Math. Phys