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Representation Theory and its Applications in Physics
No full textRepresentation theory is a branch of mathematics that allows us to represent elements of a group as elements of a general linear group of a chosen vector space by means of a homomorphism. The group elements are mapped to linear operators and we can study the group using linear algebra. This ability is especially useful in physics where much of the theories are captured by linear algebra structures. This thesis reviews key concepts in representation theory of both finite and infinite groups. In the case of finite groups we discuss equivalence, orthogonality, characters, and group algebras. We discuss the importance and implications of Maschke’s and Schur’s theorem. Our study of finite group representations is concluded by an example of an application of the representation of the permutation group S3 to a system of particles. In the case of infinite groups, we devote all our attention to Lie group representations as applications of representation theory in quantum physics predominantly rely on them. We develop a way to build operators that could be used to capture invariant properties by means of representations of unitary Lie groups
The Effects of Personality and Risk Preferences on Effort-Based Behavior: A Game Theoretic Approach
No full textOur personality and preferences play a major role in the decisions we make in our everyday lives. Drawing from literature exploring how people innovate under different scenarios (Dubina, 2013), the present study expanded this topic to include any scenario where there is incentive to free-ride off of another’s effort. I designed a study in which participants (N=73) were asked to complete the Big 5 personality questionnaire, a cognitive reflection task, an altruism elicitation task, and a risk elicitation task, then were randomly paired with another participant to complete four different rounds of a public goods game. Each round of the game involved a unique incentive structure, in which participants could choose to be generous or to free-ride off of their partner’s contributions. Participants were more likely to act generously in a cooperative environment than a control environment, and were even more likely to act generously under a competitive environment. Additionally, altruistic participants were more likely to act generously across all rounds. However, personality traits and risk preferences did not play a major role in participants’ behavior in the public goods game. These findings provide some insights into which factors drive human behavior and decision making when there is incentive to free-ride, and specifically show that economic incentives are the strongest driving force in these scenarios
Growing Green: The Barriers to Sustainability in the Recreational Cannabis Industry in the State of Maine
No full textThis study is an exploration of the recreational cannabis industry in the state of Maine, specifically exploring environmental, social, and economic sustainability and the barriers that the industry faces in order to be more sustainable. Studies about the recreational cannabis industry are extremely limited due to the plants’ lack of federal legalization and limited information. While this study works to examine sustainability in the industry, it also serves as a baseline or even an entryway into the field of cannabis research. As cannabis makes strides into the business world and starts developing a status as a cash crop in many states that have legalized it, it becomes more relevant economically. This, along with many reasons surrounding the increasing popularity of cannabis, show that research in this field needs to be conducted regardless of its legalization status
Illuminated Histories
No full textArtist Maggie Libby ’81 unearths the hidden histories of Colby women with their portraits
The Multifront Battle Waged Against Female Autonomy: A Comparative Study of Ancient Medical and Literary Texts
No full textMale authors have long waged a multifront campaign against female independence. In this thesis, I focus on two specific fronts: literary and medical texts of the Classical Greek period. This thesis intends to explore the varying strategies in a selection of works, employed to reinforce prescribed gender norms. I approach this with a feminist lens to critique attempts made by elite educated Greek men to define what a woman ought to be like. I do not, however, explore every single tactic a medical and literary writer has applied to uphold patriarchal norms. My two body chapters revolve respectively around two texts: the Hippocratic Corpus and Euripides’ Medea. I, of course, draw upon scholarly sources to strengthen my argument, and I also include other Medea texts from the Classical period to illustrate the consistent anxiety toward an autonomous, active woman
The Colby Echo (April 21, 2022)
No full textPublished by the students of Colby College since 1877, The Colby Echo is the weekly, editorially independent student-run newspaper of Colby College in Waterville, Maine. Published monthly, 1877-1886; semi-monthly; 1886-1897; and weekly during the academic year, 1898-present
The Colby Echo (December 8, 2022)
No full textPublished by the students of Colby College since 1877, The Colby Echo is the weekly, editorially independent student-run newspaper of Colby College in Waterville, Maine. Published monthly, 1877-1886; semi-monthly, 1886-1897; and weekly during the academic year, 1898-present