3D scalar model as a 4D perfect conductor limit: Dimensional reduction and variational boundary conditions
- Physics Department, Bishop's University, 2600 College Street, Sherbrooke, Quebec, J1M 0C8 (Canada)
- Kavli Institute for Theoretical Physics, University of California, Kohn Hall, Santa Barbara, California 93106 (United States)
- Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario, M5S 3H4 (Canada)
Under dimensional reduction, a system in D spacetime dimensions will not necessarily yield its D-1-dimensional analog version. Among other things, this result will depend on the boundary conditions and the dimension D of the system. We investigate this question for scalar and Abelian gauge fields under boundary conditions that obey the symmetries of the action. We apply our findings to the Casimir piston, an ideal system for detecting boundary effects. Our investigation is not limited to extra dimensions and we show that the original piston scenario proposed in 2004, a toy model involving a scalar field in 3D (2+1) dimensions, can be obtained via dimensional reduction from a more realistic 4D electromagnetic (EM) system. We show that for perfect conductor conditions, a D-dimensional EM field reduces to a D-1 scalar field and not its lower-dimensional version. For Dirichlet boundary conditions, no theory is recovered under dimensional reduction and the Casimir pressure goes to zero in any dimension. This ''zero Dirichlet'' result is useful for understanding the EM case. We then identify two special systems where the lower-dimensional version is recovered in any dimension: systems with perfect magnetic conductor (PMC) and Neumann boundary conditions. We show that these two boundary conditions can be obtained from a variational procedure in which the action vanishes outside the bounded region. The fields are free to vary on the surface and have zero modes, which survive after dimensional reduction.
- OSTI ID:
- 21301025
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 79, Issue 12; Other Information: DOI: 10.1103/PhysRevD.79.125018; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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