Luiz C de Albuquerque and R M Cavalcanti 2004 J. Phys. A: Math. Gen. 37 7039 doi:10.1088/0305-4470/37/27/012
Casimir effect for the scalar field under Robin boundary conditions: a functional integral approach
Luiz C de Albuquerque1 and R M Cavalcanti2
Show affiliationsIn this work we show how to define the action of a scalar field such that the 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 c1 and c2. Some special cases are discussed; in particular, we show that for some values of c1 and c2 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 λ
4 theory subject to the Robin boundary condition on a plate.
- PACS
- MSC
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81T05 Axiomatic quantum field theory; operator algebras
81T17 Renormalization group methods
46N20 Applications to differential and integral equations
81T70 Quantization in field theory; cohomological methods (See also 58D29)
- Subjects
- Dates
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Issue 27 (9 July 2004)
Received 6 November 2003, in final form 26 April 2004
Published 22 June 2004
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Casimir effect for the scalar field under Robin boundary conditions: a functional integral approach
Luiz C de Albuquerque and R M Cavalcanti 2004 J. Phys. A: Math. Gen. 37 7039
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