Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
| dc.creator | Grosse, Harald | |
| dc.creator | Wulkenhaar, Raimar | |
| dc.date | 2004-01-20 | |
| dc.date | 2004-10-04 | |
| dc.date.accessioned | 2026-07-07T10:49:49Z | |
| dc.date.available | 2026-07-07T10:49:49Z | |
| dc.description | We prove that the real four-dimensional Euclidean noncommutative ϕ^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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/hep-th/0401128 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0401128 | |
| dc.identifier | Commun.Math.Phys.256:305-374,2005 | |
| dc.identifier | doi:10.1007/s00220-004-1285-2 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/184346 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base | |
| dc.type | text |