The trace identity and the planar Casimir effect
Click here to view fulltext PDF
Permanent link:
https://www.ias.ac.in/article/fulltext/pram/066/02/0325-0344
The familiar trace identity associated with the scale transformationxΜ→ x′Μ = e-λxΜ 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.
Volume 96, 2022
All articles
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode
© 2021-2022 Indian Academy of Sciences, Bengaluru.