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Pramana

, Volume 66, Issue 2, pp 325–344 | Cite as

The trace identity and the planar Casimir effect

  • S. G. Kamath
Article

Abstract

The familiar trace identity associated with the scale transformationx Μ → x′ Μ = e x Μ on the Lagrangian density for a noninteracting massive real scalar field in 2 + 1 dimensions is shown to be violated on a single plate on which the Dirichlet boundary condition Φ(t, x1, x2 = -a) = 0 is imposed. It is however respected in: (i) 1 + 1 dimensions in both free space and on a single plate on which the Dirichlet boundary condition Φ(t, x1 = -a) = 0 holds and (ii) in 2 + 1 dimensions in free space, i.e. the unconstrained configuration. On the plate where Φ(t, x1, x2 = -a) = 0, the modified trace identity is shown to be anomalous with a numerical coefficient for the anomalous term equal to the canonical scale dimension, viz. 1/2. The technique of Bordaget al [Ann. Phys. (N.Y.),165, 162 (1985)] is used to incorporate the said boundary condition into the generating functional for the connected Green’s functions.

Keywords

Massive scalar field trace identity Casimir effect 

PACS No

11.30.-j 

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Copyright information

© Indian Academy of Sciences 2006

Authors and Affiliations

  • S. G. Kamath
    • 1
  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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