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Noncommutative quantum field theory
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DOI：10.1002/prop.201400020.png)
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We summarize our recent construction of the phi(4)-model on four-dimensional Moyal space. This is achieved by solving the quartic matrix model for a general external matrix in terms of the solution of a non-linear equation for the 2-point function and the eigenvalues of that matrix. The beta-function vanishes identically. For the Moyal model, the theory of Carleman type singular integral equations reduces the construction to a fixed point problem. The resulting Schwinger functions in position space are symmetric and invariant under the full Euclidean group. The Schwinger 2-point function is reflection positive iff the diagonal matrix 2-point function is a Stieltjes function. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Keyword:
BETA-FUNCTION
RENORMALIZATION
CONSTRUCTION
DUALITY
AXIOMS
R-4
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