Integrability and positivity in quantum field theory on noncommutative geometry

[摘要] We review a sequence of papers in which we construct the lambda phi(*4)(4)-model and the lambda phi(*3)(2,4,6)-models on noncommutative Moyal space by a common method. Thereby we show that not only the Kontsevich model lambda Phi(3) but also the lambda Phi(4)(4)-model is integrable in a certain scaling limit which corresponds to infinitely large Moyal deformation parameter. Surprisingly, this limit gives rise to Schwinger functions on commutative Euclidean space. Our explicit formulae permit us to discuss reflection positivity of these Schwinger functions. (C) 2018 Published by Elsevier B.V.

[发布日期] 2018-12-01

[效力级别]  Proceedings Paper

[关键词] Quantum field theory;Noncommutative geometry;Solvable model;Matrix model;Schwinger-Dyson equation;Reflection positivity