  Recent work on non proper-gauge degrees of freedom in the context of the
Casimir effect is reviewed. In his original paper, Casimir starts by pointing
out that, when the electromagnetic field is confined between two perfectly
conducting parallel plates, there is an additional physical polarization of the
electromagnetic field at zero value for the discretized longitudinal momentum
besides the standard two transverse polarizations at non-zero values. In this
review, the dynamics of these additional modes is obtained from first
principles. At finite temperature, their contribution to the entropy is
proportional to the area of the plates and corresponds to the contribution of a
massless scalar field in 2+1 dimensions. When the plates are charged, there is
a further contribution to the partition function from the zero mode of this
additional scalar that scales with the area but does not contribute to the
entropy. It reproduces the result obtained when the Gibbons-Hawking method is
applied to the vacuum capacitor. For completeness, a brief discussion of the
classical thermodynamics of such a capacitor is included.
