Imagine the universe consisted only of beads of different size and color on a single string, with some rules about how they would interact, combine, separate from, or bounce off one another. How would familiar notions of classical physics such as gravity or electromagnetism look like in such a universe? What about quantum phenomena? How far can one go on this quest? Is it feasible to look for a one-dimensional "theory of everything"?
This is the stuff of fundamental physics, and my goal in this course is to
- introduce students to the mathematical tools they need in order to understand these questions
- help them use those tools to find satisfactory answers to some of the questions
- give them the vocabulary they need in order to ask many more such profound questions, not just about this cartoon world, but also about the actual world we live in.
Among the topics to be considered in this course are
- joint evolution of classical particles and fields
- one-dimensional relativistic gravity
- bound states of quantum hamiltonians for hydrogenic ions
- electron-photon scattering
- emission and absorption of radiation by atoms
The emphasis will be on mathematical rigor and exact analysis. Assignments include weekly readings, in-class discussions, and a final project. Previous knowledge of physics is welcome but not required. Mathematical knowledge at the level of Calculus 3 and Linear Algebra (or permission of instructor) is required. Familiarity with computational software such as Matlab, Maple, or Mathematica is strongly preferred.
About Professor Tahvildar-Sadeh
https://sites.math.rutgers.edu/~shadit/