Ultraviolet Finite Quantum Field Theory on Quantum Spacetime

We show that the optimal degree of approximate coincidence can be defined by the evaluation of a conditional expectation which replaces each function of qj − qk by its expectation value in optimally localized

D. Bahns; S. Doplicher; K. Fredenhagen; G. Piacitelli

2015

Scholarcy highlights

  • Spacetime quantization was proposed earlier than renormalization theory as a possible way of regularizing quantum field theory
  • We show that the S-matrix is term by term finite
  • Motivation was given : the concurrence of the principles of quantum mechanics and of classical general relativity leads to spacetime uncertainty relations; the natural geometric background that implements those relations is a noncommutative model of spacetime
  • In order to give localization in spacetime an operational meaning, the energy transfer associated to the localization of an event by the Heisenberg uncertainty principle should be limited so that the generated gravitational field does not trap the event itself inside an horizon; otherwise the observation would be prevented
  • The proof is complete by, if we show that the function W is in L2(R3(r+s))
  • We conclude our discussion by showing that it is not possible to absorb the time ordering in Feynman propagators, i∆F =, φ(y)]Ω), as one usually does in the framework of ordinary local theories

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