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Casimir effect for the scalar field under Robin boundary conditions: A functional integral approach

Luiz C. de Albuquerque·R. M. Cavalcanti
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Abstract

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 $λϕ^4$ theory submitted to Robin boundary condition on a plate.

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Luiz C. de Albuquerque, R. M. Cavalcanti. 2004-06-01. Casimir effect for the scalar field under Robin boundary conditions: A functional integral approach. https://doi.org/10.1088/0305-4470%2F37%2F27%2F012

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