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Renormalisation of scalar quantum field theory on noncommutative ℝ 4
Author(s) -
Grosse H.,
Wulkenhaar R.
Publication year - 2005
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200410231
Subject(s) - noncommutative geometry , noncommutative quantum field theory , commutative property , quantum field theory , harmonic oscillator , scalar field theory , scalar field , scalar (mathematics) , mixing (physics) , physics , effective action , action (physics) , mathematical physics , field (mathematics) , field theory (psychology) , quantum mechanics , quantum , theoretical physics , mathematics , quantum gravity , pure mathematics , geometry
We give the main ideas our proof that the noncommutative ϕ 4 ‐model is renormalisable to all orders. Compared with the commutative case, the bare action of relevant and marginal couplings contains necessarily an additional term: an harmonic oscillator potential in the free field action which solves the UV/IR‐mixing problem.