Directed Reading Programs
The Physics Directed Reading Program at UC Berkeley pairs graduate and undergraduate students to do a semester-long reading project.
Ruihao Xiao: Alice's Adventures in QFT: Renormalization Group Flow, Fall 2022
We studied together RG flow in scalar field theories following closely the Wilsonian point of view, as shown for example in Costello's book. We did the explicit computations of scalar effective actions to one loop, focusing on elucidating its non-local behavior. We also explored local renormalization group flow, which allowed us to compute beta functions in scalar field theories as well. Finally, we studied non-linear sigma models and recovered the classic result that their beta functions are governed by Ricci flow. This is the fundamental input to one of the important connections between strings and gravity. The slides can be found here and the full video of the presentation here.
Yoonsang Kim: Axioms of Quantum Mechanics, Spring 2022
We journeyed through an axiomatic point of view towards quantum mechanics. For this we built a solid foundation in linear algebra, which allowed us to state the von Neumann-Dirac axioms of quantum theory in the context of finite-dimensional Hilbert spaces. We then saw how to use the experimental input of the Stern-Gerlach experiment to develop an essentially unique theory of spin-1/2 particles. Finally, we discussed some generic features of physical theories and saw how C*-algebras could be a unifying tool in the development of these. The slides can be found here.
Kishan Jani: The Geometric Adventures of Particles, Spring 2022
We explored the applications of supersymmetric quantum mechanics to geometry. For the first part, we reviewed the basics of de Rham cohomology, both in the context of differential geometry and of electromagnetism. For the second, we explored the supersymmetric sigma model in one dimension. In particular, we saw how to implement its perturbation theory to obtain a first approximation to the de Rham cohomology of its target. The slides can be found here.
Shiyong Guo: Canonical Quantization of 2D Abelian BF Theory, Fall 2021
We did a canonical analysis of 2D abelian BF theory. We reviewed how this theory presents a holographic duality to the quantum mechanics of a particle moving on the group manifold. The main analysis was done on a spacetime with the topology of a square and with the structure group R. The case of cylindrical topologies and the structure group U(1) was also discussed. Moreover, although canonical, the analysis was done in a fully covariant manner thanks to the covariant phase space formalism. The notes used for the blackboard presentation can be found here.
Joshua Ho: Statistical Mechanics via Information Theory, Fall 2021
We studied the principles of statistical mechanics from the point of view of information theory as put forward by E. T. Jaynes. These were exemplified through a detailed study of the ideal gas. Derivations of the equipartition theorem and the ideal gas law were performed, both in the microcanonical and canonical ensembles. The notes used for the blackboard presentation can be found here.
Snehaa Ganesh Kumar: Feynman and Gauss Doing Combinatorics, Spring 2021
We developed the theory of Feynman diagrams as a method of solving Gaussian integrals. This was done using a proof of Wick's lemma based on the Schwinger-Dyson equation. We studied applications in combinatorics and quantum field theory, including a brief discussion of the heat-kernel method to renormalize scalar field theories. The presentation can be found here.