CASIMIR EFFECT IN FOUR SITUATIONS { INCLUDING A NONCOMMUTATIVE TWO-SPHERE

A computation of the Casimir e®ect for a real scalar ¯eld in four situations: on a segment of a line, on a circle and on both standard commutative and noncommuta-tive two-spheres is presented. The main aim of this paper is to discuss the Casimir energy on a noncommutative sphere within the theory with commutative time. A discussion of the (non)commutative cylinder is also given. PACS numbers: 03.70.+k, 11.10.-z UDC 537.8