Accounting for the finiteness of the Higgs-boson mass in the 3D Georgi-Glashow model

(2+1)-dimensional Georgi-Glashow model is explored in the regime when the Higgs boson is not infinitely heavy, but its mass is rather of the same order of magnitude as the mass of the W boson. In the weak-coupling limit, the Debye mass of the dual photon and the expression for the monopole potential are found. The cumulant expansion applied to the average over the Higgs field is checked to be convergent for the known data on the monopole fugacity. These results are further generalized to the SU(N)-case. In particular, it is found that the requirement of convergence of the cumulant expansion establishes a certain upper bound on the number of colours. This bound, expressed in terms of the parameter of the weak-coupling approximation, allows the number of colours to be large enough. Finally, the string tension and the coupling constant of the so-called rigidity term of the confining string are found at arbitrary number of colours.Comment: 9 pages, LaTeX2e, no figure

Noncommutative Kn\"{o}rrer periodicity and noncommutative Kleinian singularities

We establish a version of Kn\"{o}rrer's Periodicity Theorem in the context of noncommutative invariant theory. Namely, let $A$ be a left noetherian AS-regular algebra, let $f$ be a normal and regular element of $A$ of positive degree, and take $B=A/(f)$. Then there exists a bijection between the set of isomorphism classes of indecomposable non-free maximal Cohen-Macaulay modules over $B$ and those over (a noncommutative analog of) its second double branched cover $(B^\#)^\#$. Our results use and extend the study of twisted matrix factorizations, which was introduced by the first three authors with Cassidy. These results are applied to the noncommutative Kleinian singularities studied by the second and fourth authors with Chan and Zhang.Comment: Numerous typos fixed, removed unnecessary finite order hypothesi

The gamma rays from celestial objects

This Thesis describes and discusses the results obtained from observations of the astronomical objects Cygnus X-3 and the Crab Pulsar, made during 1981 and 1982 using the Very High Energy (VHE) Gamma Ray Astronomy Facility of the University of Durham. Following an introductory chapter, chapter two describes the observational technique used for the work (known as the 'Atmospheric Cerenkov Technique') and chapter three describes in some detail the design, construction and operation of the equipment. Chapter four summarises the data taken during the course of the observations, whilst chapter five describes the analysis techniques used in the examination of this data. Chapter six presents the results derived from these analyses and, finally, chapter seven discusses their implications, both for the objects themselves and for the field of Astrophysics generally. Unless otherwise stated, the Author has either been principally responsible for, or has played an important part in the production of, all the work reported in this Thesis

Higgs-inspired corrections to the RG flow in the finite-temperature 3D Georgi-Glashow model and its SU(N)-generalization

The Berezinsky-Kosterlitz-Thouless (BKT) RG flow in the ensemble of monopoles existing in the finite-temperature (2+1)D Georgi-Glashow model is explored in the regime when the Higgs field is not infinitely heavy, but its mass is rather of the same order of magnitude as the mass of the W-boson. The corrections to the standard RG flow are derived to the leading order in the inverse mass of the Higgs boson. According to the obtained RG equations, the scaling of the free-energy density in the critical region and the value of the critical temperature of the phase transition are found to be unaffected by the finiteness of the Higgs-boson mass. The evolution of the Higgs mass itself is also investigated and shown to be rather weak, that enables one to treat this parameter as a constant. The same analysis is further performed in the SU(N)-case at N>2, where the RG invariance is demonstrated to hold only approximately, in a certain sense. Modulo this approximation, the critical behaviour of the SU(N)-model turns out to be identical to that of the SU(2)-one.Comment: 12 pages, LaTeX2e, no figure

Understanding differences in underrepresented minorities and first-generation student perceptions in the introductory biology classroom

We used quantitative methods to better understand the perceptions of students in an introductory biology course (Biology 101) at a small, liberal arts college (SLAC) that is also a primarily white institution (PWI). In pre/post surveys, we asked students questions related to their attitudes and beliefs about their professor, classmates, and Biology 101. We were especially interested in the responses and outcomes of underrepresented minorities (URM) and first-generation (FG) students. Our findings suggest URM and FG students have a decreased sense of belonging and increased perceptions of exclusion and differential treatment due to race. These findings can explain, in part, the disparity in Biology 101 grade and STEM (science, technology, engineering, and math) attrition