Graduation Year
2017
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Dagan Karp
Reader 2
Stefan Mendez-Diez
Terms of Use & License Information
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 License
Rights Information
© 2017 Aaron R Bagheri
Abstract
Supersymmetry is a theoretical model of particle physics that posits a symmetry between bosons and fermions. Supersymmetry proposes the existence of particles that we have not yet observed and through them, offers a more unified view of the universe. In the same way Feynman Diagrams represent Feynman Integrals describing subatomic particle behaviour, supersymmetry algebras can be represented by graphs called adinkras. In addition to being motivated by physics, these graphs are highly structured and mathematically interesting. No one has looked at the Jacobians of these graphs before, so we attempt to characterize them in this thesis. We compute Jacobians through the 11-cube, but do not discover any significant discernible patterns. We then dedicate the rest of our work to generalizing the notion of the Jacobian, specifically to be sensitive to edge directions. We conclude with a conjecture describing the form of the directed Jacobian of the directed $n$-topology. We hope for this work to be useful for theoretical particle physics and for graph theory in general.
Recommended Citation
Bagheri, Aaron R., "Classifying the Jacobian Groups of Adinkras" (2017). HMC Senior Theses. 102.
https://scholarship.claremont.edu/hmc_theses/102
