Vacuum energy for static, cylindrically symmetric systems
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In my previous thesis for the Undergraduate Research Scholars program I have calculated, both in terms of the scalar field and in terms of the cylinder kernel, the components of the stress-energy tensor of a quantized scalar field for a static, cylindrically symmetric system in the case of locally flat space. I then took these components and expressed them in terms of the known cylinder kernel in cylindrical coordinates. Using these results, I examine the vacuum energy density and pressure in some detail for several different cylindrically symmetric space-times. Results are presented for point-splitting along the t direction, and also for point-splitting along z. Geometries studied include flat space, a cone with various deficit angles, an infinite wedge, and the infinite-sheeted Sommerfeld-Dowker manifold. For all of these cases, the energy density and three pressure components are given for xi = 1/4 coupling, and the correction terms for other values of xi are given as well.
Trendafilova, Cynthia (2012). Vacuum energy for static, cylindrically symmetric systems. Honors and Undergraduate Research. Available electronically from