Algebra Commons^™

Algebraic Tunnelling, Gaurab Sedhain

2023 REYES Proceedings

We study the quantum phenomenon of tunnelling in the framework of algebraic quantum theory, motivated by the tunnelling aspects of false vacuum decay. We see that resolvent C*-algebra, proposed relatively recently by Buchholz and Grundling rather than Weyl algebra provides an appropriate framework for treating the dynamics of non-free quantum mechanical system as an algebraic automorphism. At the end, we propose to investigate false vacuum decay in algebraic quantum field theoretic setting in terms of the two-point correlation function which gives us the tunneling probability, with the corresponding C*-algebraic construction.

Fast Multipole Method Using Cartesian Tensor In Beam Dynamic Simulation, He Zhang, He Huang, Rui Li, Jie Chen, Li-Shi Luo

Mathematics & Statistics Faculty Publications

The fast multipole method (FMM) using traceless totally symmetric Cartesian tensor to calculate the Coulomb interaction between charged particles will be presented. The Cartesian tensor based FMM can be generalized to treat other non-oscillating interactions with the help of the differential algebra or the truncated power series algebra. Issues on implementation of the FMM in beam dynamic simulations are also discussed. © 2017 Author(s).

Epistemic Strategies For Solving Two-Dimensional Physics Problems, Mary Elyse Hing-Hickman

Physics Theses & Dissertations

An epistemic strategy is one in which a person takes a piece of knowledge and uses it to create new knowledge. Students in algebra and calculus based physics courses use epistemic strategies to solve physics problems. It is important to map how students use these epistemic strategies to solve physics problems in order to provide insight into the problem solving process.

In this thesis three questions were addressed: (1) What epistemic strategies do students use when solving two-dimensional physics problems that require vector algebra? (2) Do vector preconceptions in kinematics and Newtonian mechanics hinder a student's ability to apply the …