In the Curci-Ferrari model, the non-Abelian Casimir energy between magnetic-conductor plates is 3/2 times that for electric-conductor plates, and the massless limit is discontinuous (vDVZ-like), with the same pattern in 2+1D with factor 2.
Scalar field theory under Robin boundary conditions: two-point function and energy-momentum tensor
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abstract
We reconsider four-dimensional scalar field theory in presence of Robin boundary conditions on two parallel plates. These boundary conditions are directly imposed in the path integral definition of the theory via auxiliary fields living on the plates. We discuss how this leads to boundary corrections to the standard energy momentum tensor operator. Via a dimensional reduction to an effective three-dimensional boundary theory, we compute the Casimir energy in terms of the plate separation and the two Robin parameters, as well as the scalar field propagator in the presence of the plates. Coincidentally, the boundary contribution vanishes in the expectation value for the vacuum energy, thereby giving results in full accordance with other energy expressions in the literature for the same setup. We also discuss for which values of the Robin parameters this energy is real-valued.
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Non-Abelian Casimir energy in the Curci-Ferrari model through a functional approach
In the Curci-Ferrari model, the non-Abelian Casimir energy between magnetic-conductor plates is 3/2 times that for electric-conductor plates, and the massless limit is discontinuous (vDVZ-like), with the same pattern in 2+1D with factor 2.