Grant: Subatomic Physics Envelope - Individual

We apply the techniques of quantum field theory to different physical systems under various external conditions. Our first system consists of a Georgi-Glashow model (composed of a triplet of scalar fields and SO(3) non-Abelian gauge fields) conformally coupled to gravity. We have already shown in a previous work that magnetic monopole solutions in asymptotically Anti-de Sitter (AdS) spacetime exist in this system. In this proposal we break the conformal symmetry by adding quantum matter corrections to the action leading to the conformal anomaly. Our preliminary analysis shows that an Einstein-Hilbert term (General Relativity), a cosmological constant and massive scalars, which do not appear in the original action, emerge after an expansion of the action about the non-trivial vacuum and dominate the low energy or long distance regime. The conformal anomaly fixes the scale and we anticipate that the gravitational constant G, the cosmological constant and the mass of the scalars can be expressed in terms of the parameters of the theory. We recently developed a novel multidimensional cut-off technique that yields explicit expressions for the finite and cut-off dependent part of the Casimir energy under Dirichlet and Neumann boundary conditions. The formulae are highly useful and have been applied to the Casimir piston, a topic of great current interest. In this proposal we extend our D-dimensional Casimir piston analysis to include the significant effects of finite conductivity and temperature corrections both of which are of experimental interest in 3+1 dimensions. Quantum fluctuations of the quasiparticle vacuum in a zero-temperature Bose-Einstein condensate (BEC) offer us a unique opportunity to study the Casimir effect for a field other than the usual electromagnetic field. In a previous work we studied the Casimir effect in a homogeneous BEC. In this proposal we go beyond a homogeneous BEC and study the Casimir effect of a non-homogeneous weakly interacting BEC constrained to one small and two large dimensions via a trapping potential V. This system reduces to two coupled nonlinear differential equations containing the quantum fluctutation field and the condensate field.