AAWSAP DIRD, Quantum Tomography of Negative Energy States in the Vacuum, January 2011

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Casimir
Vacuum
plates
fluctuations
Figure 2. Schematic of the Casimir Effect.
It turns out that there are many different types of Casimir effects found in quantum
field theory [20-22, 26-28, 51]. For example, if one introduces a single infinite plane
conductor into the Minkowski (flat spacetime) vacuum by bringing it adiabatically from
infinity so that whatever quantum fields are present suffer no excitation but remain in
their ground states, then the vacuum (electromagnetic) stresses induced by the
presence of the infinite plane conductor produces a Casimir effect. This result holds
equally well when two parallel plane conductors (with separation distance d) are
present, which gives rise to the familiar Casimir effect inside a cavity. Note that in both
cases, the spacetime manifold is made incomplete by the introduction of the plane
conductor boundary condition(s). The vacuum region put under stress by the presence
of the plane conductor(s) is called the Casimir vacuum. The generic expression for the
energy density of the Casimir effect is PCE =- Ahcd-4 , where A= C,(D)/8rr-2 in
spacetimes of arbitrary dimension O [20-22]. The appearance of the zeta-function (,(D)
is characteristic of expressions for vacuum stress-energy tensors, T.J:i~ .t t t In our
familiar 4-dimensional spacetime (0 = 4) we have that A = rc2/720. To calculate T_J:i~
for a given quantum field is to calculate its associated Casimir effect.
We should also point out that the methods used to obtain the quantum vacuum
electromagnetic T;~~ between parallel plane conductors can also be used when the
conductors are not parallel but are joined together along a line of intersection. If the
conductors have curved surfaces instead, then one obtains results that are similar to
the case of intersecting conductors. These geometries have also been evaluated for the
ttt The Greek tensor indices (µ, v = 0...3) denote spacetime coordinates, >l'...x3, such that xt...x 3 = space
coordinates and x0 "' time coordinate. Note in general that T00 = p E (field energy density).
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