Quantization of the Nonlinear Sigma Model Revisited

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space. We show that there are no anomalies in case (i) and that (ii) is also anomaly-free under additional assumptions on the target homogeneous space, in agreement with the work of Friedan. We carry out some explicit computations for the $O(N)$-model. Finally, we show how a suitable notion of the renormalization group establishes the Ricci flow as the one loop renormalization group flow of the nonlinear sigma model.Comment: 51 page

A Divine Selection: An Exegetical Analysis of Vocational Calling

Within Christian circles, the ‘calling’ of the vocational minister is frequently abused and misunderstood and muddled by the lack of Scriptural evidence for the overused term. The focus of this research is to observe first, the current cultural climate surrounding the nature of calling, and second, to compare this understanding to the authoritative Scriptural teaching on the subject in both the Old and New Testaments. This analysis reveals that the “internal” vocational call to minister is absent from the Bible and must be replaced by an alternative the Scripture directly teaches. It is concluded that God gives man the desire to become a minister but does not audibly select leaders in the manner of biblical characters

Twitter: a Platform for Political Discourse or Social Networking

Previous research on new media has largely focused on the potential media effects of alternative news sources on their viewers. The effects of these studies have been limited, however, to the narrow audiences targeted by the increasingly polarizing alternative news sources. The advent and popularization of social networks has provided a reason to suspect that, for the first time, alternative news sources are making their way to the mainstream general public. In this study, I examine a new political and media environment that encourages the interaction between the politically inattentive public and polarized and alternative news sources – a link that contains numerous implications of previously inapplicable studies. I elaborate on previous literature pertaining to social networking’s capacity to operate as both a social networking vehicle and as a platform for further political debate by incorporating previous research that suggests an inherent polarization in alternative news sources with other studies that have highlighted the majority of society’s political inattentiveness. The results of my study suggest that Twitter users – the majority of them being politically inattentive – are more likely to be exposed to polarizing alternative news sources as opposed to mainstream news coverage when seeking out issue-based news items. By discovering a previously undetected link between polarized alternative news sources and the politically inattentive, this paper opens the door for future studies to study the effects of polarized reportage on the politically inattentive and the relationship between social networking and the traditional mainstream media

Lagrangian correspondences and Donaldson's TQFT construction of the Seiberg-Witten invariants of 3-manifolds

Using Morse-Bott techniques adapted to the gauge-theoretic setting, we show that the limiting boundary values of the space of finite energy monopoles on a connected 3-manifold with at least two cylindrical ends provides an immersed Lagrangian submanifold of the vortex moduli space at infinity. By studying the signed intersections of such Lagrangians, we supply the analytic details of Donaldson's TQFT construction of the Seiberg-Witten invariants of a closed 3-manifold.Comment: 43 pages. Revised version. To appear in Algebraic & Geometric Topolog