Noncommutative Field Theory

We propose noncommutative space-time and a method to construct noncommutative field theory in terms of a covariant ★-product Moyal algebra and to study those physical and mathematical consequences. We consider noncommutative quantum electrodynamics. The prescription involves calculating the trace-like averaging procedure of noncommutative spacetime, leading to the nonlocal theory. From experimental data on testing the local theory it follows that θ ≲ 7 ⋅ 10−32m2, where θ is the dimensionful scale of the tensor θμν characterizing noncommutative properties of spacetime arising from low-energy limit of string theories.