Geometric Finiteness and Non-quasinormal Modes of the BTZ Black Hole

The BTZ black hole is geometrically finite. This means that its three dimensional hyperbolic structure as encoded in its metric is in 1-1 correspondence with the Teichmuller space of its boundary, which is a two torus. The equivalence of different Teichmuller parameters related by the action of the modular group therefore requires the invariance of the monodromies of the solutions of the wave equation around the inner and outer horizons in the BTZ background. We show that this invariance condition leads to the non-quasinormal mode frequencies discussed by Birmingham and Carlip.Comment: 8 Pages, Latex file, minor changes in the text, journal versio

It Hastened What We All Fought For, the End of the War: General Sherman\u27s Campaigns through Atlanta, Georgia, and the Carolinas and How They Impacted the Civil War

“It hastened what we all fought for, the end of the war: General Sherman’s campaigns through Atlanta, Georgia, and the Carolinas and how they impacted the Civil War” is my collection of research of the importance of Sherman’s campaigns through Atlanta, Georgia, and the Carolinas to bring the end of the war. My project is in fulfillment of the History 451: Proseminar within the requirements of a Bachelor’s Degree in history. My thesis paper covers those three campaigns and their importance in bringing the Civil War to an end. I have used primary and secondary evidence to provide facts and to support the importance of Sherman in the Civil War. Although Sherman’s role is a controversial topic of morality and necessity, I tried only to provide evidence and discussion for how it helped lead the Union to a victory on April 9, 1865. My goal was to offer analysis of 1864 and why Sherman’s marches were required.. Grant could not secure a victory around Richmond, Confederate forces attacked Washington DC and through all this a rising Pro-Peace Democratic Party led by former General, George McClellan threatened the re-election of Abraham Lincoln. It was not until General Sherman’s success at Atlanta that hope shone in the Union. From Atlanta and throughout Sherman’s remaining campaigns, he famously brought the war to Southern civilians making the war not only a physical war, but a psychological one as well. Sherman’s efforts against the Confederate forces and the Southern morale were imperative so the North could rise victorious in April, 1865

A Renormalized Supersymmetry in the Topological Yang-Mills Field Theory

We reconsider the algebraic BRS renormalization of Witten's topological Yang-Mills field theory by making use of a vector supersymmetry Ward identity which improves the finiteness properties of the model. The vector supersymmetric structure is a common feature of several topological theories. The most general local counterterm is determined and is shown to be a trivial BRS-coboundary.Comment: 18 pages, report REF. TUW 94-10 and UGVA-DPT 1994/07-85

Discrete Quantum Field Theories and the Intersection Form

It is shown that the standard mod-$p$ valued intersection form can be used to define Boltzmann weights of subdivision invariant lattice models with gauge group $Z_{p}$. In particular, we discuss a four dimensional model which is based upon the assignment of field variables to the $2$-simplices of the simplicial complex. The action is taken to be the intersection form defined on the second cohomology group of the complex, with coefficients in $Z_{p}$. Subdivision invariance of the theory follows when the coupling constant is quantized and the field configurations are restricted to those satisfying a mod-$p$ flatness condition. We present an explicit computation of the partition function for the manifold $\pm CP^{2}$, demonstrating non-triviality.Comment: 10 pages, Latex, ITFA-94-1