**1) Introduction and Motivation**

We would like to call attention to a new class offered this winter/spring 2014 quarter, being taught jointly by Prof. Daniel Ruberman in Mathematics and Prof. Albion Lawrence in Physics. This is being listed jointly as Physics 202a (Quantum Field Theory) and Math 221b (Topics in Topology). It is being team-taught under the auspices of the Brandeis Geometry and Dynamics IGERT program.

This course aims to introduce basic notions of fiber bundles and connections on them, and their application to basic physical examples in classical and quantum mechanics: especially the mechanics of deformable bodies, and Berry’s phase. The target audience is mathematics and physics students, and mathematically inclined students in physical chemistry, neuroscience, computer science, and economics. The essential principles here find applications to chemical and neural oscillators and control theory; there have even been suggestions that it is a useful language for describing currency trading.

The mathematics covered here typically appears in advanced courses on quantum and statistical field theory. However, it has much broader applicability, and the instructors felt that studying more elementary physics examples better highlighted the essential mathematics and lead to a broader perspective that would better prepare students to find new and creative uses for the mathematics. Furthermore, they allow us to teach a broader audience, as the essential physics background is straightforward and can be explained without the student needing two years of graduate-level physics courses.

This course is essentially a graduate course, but it is certainly appropriate for senior undergraduates with a solid mathematical background (math and physics majors especially). The modern mathematical language of manifolds and vector bundles will be introduced and used throughout, but with reference to physical and geometric notions. This will provide physics students with an appropriate vocabulary for further study, while mathematics students can try to grasp the intuition behind the formalism. Note that the course satisfies one of the IGERT course requirements; however, we strongly encourage non-IGERT students to enroll.

The course is scheduled to take place Mondays and Wednesdays from 2-3:20pm. [Read more…]