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A Solvable Four-Dimensional QFT

In: Quantum Mathematical Physics

Author

Listed:
  • Harald Grosse

    (Universität Wien, Fakultät für Physik)

  • Raimar Wulkenhaar

    (Mathematisches Institut der Westfälischen Wilhelms-Universität)

Abstract

We review a sequence of papers in which we show that the quartic matrix model with an external matrix is exactly solvable in terms of the solution of a non-linear integral equation. The interacting scalar model on four-dimensional Moyal space is of this type, and our solution leads to the construction of Schwinger functions. Taking a special limit leads to a QFT on $$\mathbb{R}^{4}$$ which satisfies growth property, covariance and symmetry. There is numerical evidence for reflection positivity of the 2-point function for a certain range of the coupling constant.

Suggested Citation

  • Harald Grosse & Raimar Wulkenhaar, 2016. "A Solvable Four-Dimensional QFT," Springer Books, in: Felix Finster & Johannes Kleiner & Christian Röken & Jürgen Tolksdorf (ed.), Quantum Mathematical Physics, edition 1, pages 137-161, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-26902-3_8
    DOI: 10.1007/978-3-319-26902-3_8
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