Casimir effect in four simple situations - including a noncommutative two-sphere

A computation of the Casimir effect for a real scalar field in four situations: on a segment of a line, on a circle and on both standard commutative and noncommutative two-spheres is given in this paper. The main aim of this paper is to discuss the Casimir energy on the noncommutative sphere within the theory with commutative time. The comparison with the noncommutative cylinder is also done.Comment: 15 pages, 5 figure

Study of the Coleman - de Luccia instanton of the second order

We study the second order Coleman - de Luccia instanton which appears as the curvature of the effective potential reaches a sufficiently large value. We show how one can find the approximative formula for this instanton by perturbative expansion in the case when the second derivative of the effective potential divided by the Hubble parameter squared is close to -10, and we perform a numerical study of this instanton in the case of quasi-exponential potential.Comment: three pages, one figur

Casimirov efekt u četiri slučaja, uključivši nekomutativnu dvosferu

A computation of the Casimir effect for a real scalar field in four situations: on a segment of a line, on a circle and on both standard commutative and noncommutative 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.Daju se ishodi računa Casimirovog efekta za realno skalarno polje u četiri slučaja: na dužini, na kružnici, te na komutativnoj i nekomutativnoj dvosferi. Glavni je cilj ovog rada raspraviti Casimirovu energiju na nekomutativnoj sferi u okviru teorije s komutativnim vremenom. Raspravlja se također (ne)komutativni valjak