I'm studying noncommutative (quantum) field theory, and I have confusion need to be clear. I'm reading Szabo's and Douglas's .pdf of noncommutative QFT.

As I understand, in the book they just construct Field Theories in noncommutative spacetime, which have action functional (of Weyl operator or of normal function with star-product).

What is the relation between this Field Theory in NC spacetime and Field Theory in normal spacetime? Can we quantize the field theory in NC spacetime (as we quantize the field theory in normal spacetime)? (Field theory in NC spacetime has the quantized spacetime, but not quantized field, doesn't it?) I cannot find materials about the Quantized Field theory in NC spacetime. (just field theory in NC spacetime.)

  • $\begingroup$ Just google search "Quantum Field Theory Noncommutative space arxiv" and/or "Quantum Field Theory Noncommutative space connes" for the approach by Alain Connes $\endgroup$ – Trimok Jul 24 '14 at 9:28
  • $\begingroup$ I cannot really understand all the complicated noncommutativ geometry. It would be really good just to understand the relation between the canonical QFT and the Weyl-symbol field theory in NC spacetime. I'm not taking any further $\endgroup$ – Leaning Jul 24 '14 at 10:55
  • 1
    $\begingroup$ Maybe the Chapter $3$, and especially Chapter $3.3$ of this Szabo's paper might interest you. $\endgroup$ – Trimok Jul 25 '14 at 8:16

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