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.)