Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-05-26
J.Math.Phys. 42 (2001) 1974-1986
Physics
High Energy Physics
High Energy Physics - Theory
REVTeX, 16 pages, 1 figure in a separate fig1.eps file; revised version accepted for publication in J. Math. Phys
Scientific paper
10.1063/1.1361064
The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of the cylinder and by considering only a half of this configuration. All the surfaces, including the cutting plane, are assumed to be perfectly conducting. The zeta functions for scalar massless fields obeying the Dirichlet and Neumann boundary conditions on the semi-circular cylinder are constructed exactly. The sum of these zeta functions gives the zeta function for electromagnetic field in question. The relevant plane problem is considered also. In all the cases the final expressions for the corresponding Casimir energies contain the pole contributions which are the consequence of the edges or corners in the boundaries. This implies that further renormalization is needed in order for the finite physical values for vacuum energy to be obtained for given boundary conditions.
Lambiase Gaetano
Nesterenko V. V.
Scarpetta Gaetano
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