Noncommutative quantum field theory
Copyright policy )Noncommutative quantum field theory
AbstractWe summarize our recent construction of the ϕ4‐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 β‐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.
- University of Vienna Austria
103019 Mathematical physics, Eigenvalues, singular values, and eigenvectors, EUCLIDEAN GREENS FUNCTIONS, CONSTRUCTION, RENORMALIZATION, ORDERS, PHI(4)(4) THEORY, PHI(4)-THEORY, quartic matrix model, AXIOMS, Finite-dimensional groups and algebras motivated by physics and their representations, DUALITY, Noncommutative geometry methods in quantum field theory, SPACE, 103019 Mathematische Physik, BETA-FUNCTION, Integral equations with kernels of Cauchy type, Gamma, beta and polygamma functions
103019 Mathematical physics, Eigenvalues, singular values, and eigenvectors, EUCLIDEAN GREENS FUNCTIONS, CONSTRUCTION, RENORMALIZATION, ORDERS, PHI(4)(4) THEORY, PHI(4)-THEORY, quartic matrix model, AXIOMS, Finite-dimensional groups and algebras motivated by physics and their representations, DUALITY, Noncommutative geometry methods in quantum field theory, SPACE, 103019 Mathematische Physik, BETA-FUNCTION, Integral equations with kernels of Cauchy type, Gamma, beta and polygamma functions
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