On the unitarity problem in space/time noncommutative theories

Abstract

It is shown that the violation of unitarity observed in space/time noncommutative field theories is due to an improper definition of quantum field theory on noncommutative spacetime.Comment: 7 pages; typos corrected, sign convention changed on p.

Non Local Theories: New Rules for Old Diagrams

“…We will obtain an alternative set of rules for ordinary diagrams, which contains the standard Feynman rules for the usual local theory as a special case. This complements the discussion of [7].…”

Quantum Field Theory: Where We Are

“…While these are definitely not more than crude models, in which gravity is not itself present but just motivates the localization uncertainty, it could be established that they are compatible with Quantum Field Theory; contrary to widespread hopes, however, the quantum structure of spacetime does not act as a "physical regulator" at the Planck scale for the ultraviolet behaviour of quantum field theory [27] …”

DFR Perturbative Quantum Field Theory on Quantum Space Time, and Wick Reduction

“…Since the perturbation theory described above is built on top of a Hamiltonian model, the S-matrix of the DFR φ ⋆n interaction is (formally) unitary by construction. More recent concerns about possible unitarity violation were the consequence of a too naive way of performing the time ordering prescription (see [10], and references therein; see also [11,12]). The ultraviolet regularity of a φ ⋆3 DFR model has recently been proved by Bahns [13], under a weaker prescription for averaging over σ.…”

“…As an example of this situation we mention the noncommutative analogue of the Yang-Feldman equation proposed in [10], and developed in [16,11]. Finally, see [17,18] for a different generalization of the Wick product, based on optimal localization; the resulting model is free of ultraviolet divergences.…”