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The Noncommutative Moyal-Weyl Spaces R d θ

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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

This chapter contains a detailed discussion of the Heisenberg algebra and its representation theory. Then a systematic construction of the Moyal-Weyl noncommutative spaces, in a generic non-zero magnetic field, and their scalar field theories is put forward. A self-contained discussion of two other closely related non commutative space, the noncommutative torus and the fuzzy disc, is also included.

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Notes

  1. 1.

    We note that only bounded operators subjected to some growth restriction are in fact allowed in analogy with the allowed entire functions.

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Authors and Affiliations

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

    Badis Ydri

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  1. Badis Ydri
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Ydri, B. (2017). The Noncommutative Moyal-Weyl Spaces R d θ . In: Lectures on Matrix Field Theory. Lecture Notes in Physics, vol 929. Springer, Cham. https://doi.org/10.1007/978-3-319-46003-1_2

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