Boundaries and the Casimir effect in noncommutative space-time

We calculate modifications to the scalar Casimir force between two parallel plates due to space-time noncommutativity. We devise a heuristic approach to overcome the difficulties of describing boundaries in noncommutative theories and predict that boundary corrections are of the same order as noncommutative volume corrections. Further, both corrections have the form of more conventional finite surface effects.

Figure 1

Upper plot: Casimir pressure in the commutative case (dashed line) and the noncommutative case (solid line) in units of ${\Theta }^{-4}$ as a function of the separation $L$ between the plates (in units of $\ell =\sqrt{\Theta }$). Lower plot: Percentage difference between the two Casimir pressures as a function of $L/\ell$. Only volume effects are included.