# Investigation into compactifed dimensions: Casimir energies and phenomenological aspects.

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## Abstract

A central theme in this dissertation is the notion of the quantum vacuum. To a particle physicist, the term 'vacuum' means the ground state of a theory. In general, this ground state must obey Lorentz invariance, at least with regards to 3 spatial dimensions, meaning that the vacuum must look identical to all observers. At all energies probed by experiments to date, the universe is accurately described as a set of quantum fields. If we take the Fourier transform of a free quantum field, each mode of a fixed wavelength behaves like a simple harmonic oscillator. A quantum mechanical property of a simple harmonic oscillator is that the ground state exhibits zero-point fluctuations as a consequence of the Heisenberg Uncertainty Principle. These fluctuations give rise to a number of phenomena; however, two are particularly striking. First, the Casimir Effect, which will be examined in detail in this dissertation is arguably the most salient manifestation of the quantum vacuum. In its most basic form it is realized through the interaction of a pair of neutral parallel conducting plates. The presence of the plates modifies the quantum vacuum, and this modification causes the plates to be pulled toward each other. Second is the prediction of a vacuum energy density, which is an intrinsic feature of space itself. Many attempts have been made to relate this vacuum energy to the cosmological constant Lambda, which is a common feature in modern cosmology; however, calculations are typically plagued either by divergences or by ridiculously high predictions which are far removed from observation. This chapter will first provide a brief historical review of the vacuum and then discuss in detail some of the attempts to explain the vacuum in the language of Quantum Field Theory (QFT).