Nonperturbative Quantum Field Theory and Noncommutative Geometry

  title={Nonperturbative Quantum Field Theory and Noncommutative Geometry},
  author={Johannes Aastrup and J. M. Grimstrup},
  journal={arXiv: Mathematical Physics},
  • Johannes Aastrup, J. M. Grimstrup
  • Published 2017
  • Mathematics, Physics
  • arXiv: Mathematical Physics
  • A general framework of non-perturbative quantum field theory on a curved background is presented. A quantum field theory is in this setting characterised by an embedding of a space of field configurations into a Hilbert space over $\mathbb{R}^\infty$. This embedding, which is only local up to a scale that we interpret as the Planck scale, coincides in the local and flat limit with the plane wave expansion known from canonical quantisation. We identify a universal Bott-Dirac operator acting in… CONTINUE READING
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