On the zero-point energy of elliptic-cyliindrical and spheroidal boundaries : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Theoretical Physics at Massey University, New Zealand
Zero-point energy is the energy of the vacuum. Disturbing the vacuum results in a
change in the zero-point energy. In 1948, Casimir considered the change in the zeropoint
energy when the vacuumis disturbed by two parallelmetal plates. The plates disturb
the vacuum by restricting the quantum fluctuations of the electromagnetic field.
Casimir found that the change in the zero-point energy implies that the plates are attracted
to each other. With the recent advances made in the experimental verification
of this remarkable result, theoretical interest has been rekindled. In addition to the
original parallel plate configuration, several other boundaries have been studied. In
this thesis, two novel boundaries are considered: elliptic-cylindrical and spheroidal.
The results for these boundaries lead to the conjecture that zero-point energy does
not change for small deformations of the boundary that preserve volume. Assuming
the conjecture, it is shown that zero-point energy plays a stabilizing role in quantum
chromodynamics, the leading theory of the strong interaction.