 Noncommutative quantum field theory

Noncommutative quantum field theory (NCQFT) is an extension of traditional quantum field theory where the space-time coordinates do not commute. In standard quantum field theory, the coordinates of spacetime are treated as classical operators that commute with each other. However, in noncommutative geometries, the fundamental idea is that the coordinates of spacetime satisfy a noncommutative algebra, which means that the product of two coordinates may depend on the order in which they are multiplied.