Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-11-06
J.Phys. A37 (2004) 7039-7050
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, 2 figures. Version 2: contains a new section on the renormalization of the two-point Green function in the presence
Scientific paper
10.1088/0305-4470/37/27/012
In this work we show how to define the action of a scalar field in a such a way that Robin boundary condition is implemented dynamically, i.e., as a consequence of the stationary action principle. We discuss the quantization of that system via functional integration. Using this formalism, we derive an expression for the Casimir energy of a massless scalar field under Robin boundary conditions on a pair of parallel plates, characterized by constants $c_1$ and $c_2$. Some special cases are discussed; in particular, we show that for some values of $c_1$ and $c_2$ the Casimir energy as a function of the distance between the plates presents a minimum. We also discuss the renormalization at one-loop order of the two-point Green function in the $\lambda\phi^4$ theory submitted to Robin boundary condition on a plate.
Cavalcanti Ricardo M.
de Albuquerque Luiz C.
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