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Quantum Noncommutative Phi-Four

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Lectures on Matrix Field Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 929))

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Abstract

In this chapter quantum noncommutative \(\Phi ^{4}\) theories on Moyal-Weyl spaces, the noncommutative fuzzy torus, and the fuzzy spheres S N 2 and S N 2 ×S N 2 are presented. This includes analytical results such as the UV-IR mixing, the stripe phase, the exact solution of the self-dual theory, as well as Monte Carlo results such as the phase structure on the fuzzy sphere, and the dispersion relation on the noncommutative fuzzy torus. Other results such as quantum noncommutative \(\Phi ^{4}\) theory on fuzzy S 2 ×S 2 and the Wilson renormalization group approach to noncommutative \(\Phi ^{4}\) in the Moyal-Weyl picture and in the matrix basis at the self-dual point are also briefly discussed.

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  1. Institute of Physics, BM Annaba University, Annaba, Algeria

    Badis Ydri

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Ydri, B. (2017). Quantum Noncommutative Phi-Four. In: Lectures on Matrix Field Theory. Lecture Notes in Physics, vol 929. Springer, Cham. https://doi.org/10.1007/978-3-319-46003-1_4

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