Q&A: R. Shankar on the beauty of condensed-matter physics

Yale University’s R. Shankar is known among his colleagues for his contributions to field theory in both particle and condensed-matter physics. Students around the world, however, know him from his freely available Open Yale lectures on YouTube, where the energetic theorist breaks down concepts from Newton’s laws of motion to quantum mechanics with clarity and humor. “Best professor ever!” raves one commenter on RateMyProfessors.com; another writes, “He makes you love physics.”

Shankar brings his pedagogical gifts to the textbook realm as well. In his latest book, Quantum Field Theory and Condensed Matter: An Introduction, he gives graduate students an overview of his field. In the June issue of Physics Today, Michael Stone writes that Shankar’s “gift for clear exposition is once again on display in his latest work” and says the book will be a welcome addition to many graduate programs in physics.

PT: You began your career working on quantum field theory’s applications to particle physics. Why did you move into condensed matter?

SHANKAR: There were two reasons. One was that there were problems that lay at the interface of the two subjects. A problem I had worked on in field theory had a relationship to a problem in statistical mechanics. I didn’t know that until [Princeton theoretical physicist] Alexander Polyakov, who was visiting Yale, said, “You know, these problems are connected.” I found out what the connection was, followed the statistical mechanics part of it, and found it to be so beautiful that I stopped doing particle physics and slowly moved into that field.

I also found that there are many tools of the trade that have many more applications in condensed matter than in particle physics, because there are fewer restrictions on the kind of problems you can do. When you want to study a quantum field theory that describes the world we live in, it has to have three spatial dimensions and one time. It must satisfy Albert Einstein’s relativity, and it’s also got to have a property called renormalizability, which means when you compute numbers you don’t get crazy infinite answers. Few theories satisfy all that.

But if you go to condensed matter, you can work in three spatial dimensions or two or one or even a quantum dot, which is essentially zero spatial dimensions. And the theories don’t have to satisfy relativity—it doesn’t apply to condensed-matter problems. A lot of techniques that are otherwise studied just for fun actually become real tools.

PT: Tell us about your experience writing Quantum Field Theory and Condensed Matter. I understand that it was a decade or more in the making.

SHANKAR: I will not tell you exactly how many years in the making! I can only say that if it was my kid, it would be in college. It was a difficult book to write, and therefore I kept returning to my other books on introductory physics, based on the lectures I gave at Yale [Fundamentals of Physics I and II ]. They were easier to write because I had my transcripts for the lectures. After they were done, I came back to this one and took a deep breath and finished it in a year.

Quantum Field Theory and Condensed Matter was more difficult simply because it was more advanced material. You can’t just lock yourself in a room and derive all the formulas from memory. You have to go to the library to consult the literature and cite all the right articles. More important, you have to get the history of the subject right because many of the founders are still alive, and you want to be careful to give credit where it’s due.

PT: You mentioned the two textbooks you’ve written to accompany your online Fundamentals of Physics course for the Open Yale website. How did you get involved with the Open Yale program?

SHANKAR: Around 2007 Yale started this program of recording some select introductory courses, mostly in the humanities and maybe one or two in the sciences. They would send a video crew to tape the whole thing—with all the questions, all the mistakes, everything—and they would put it online, with free access to anybody who wanted it. Peter Salovey, who was dean at the time, said, “Do you mind if we tape your lectures?” And I said, “I’ve not met a camera I did not like!” Then they decided that part one was received extremely well, so they let me go back and teach part two.

PT: Why did you decide to write your own textbooks to accompany the online course?

SHANKAR: The blackboard treatment is fine, but in a book all of the equations are typeset in a nice script, and all the derivations are given in their final and perfect form. My goal was to write a book that wasn’t so expensive, because the price of textbooks has become astronomical. I tried to keep the production as simple as possible, and that kept the price under $25.

PT: What are you working on right now?

SHANKAR: When I wrote the Fundamentals of Physics books, I didn’t include many exercises. I thought that was one way to keep the price down; the Open Yale website has problems with solutions that anybody can look at. Then I found out that most instructors seem to want a much larger number of problems, and problems of increasing difficulty. In the next edition, there will be maybe 50 or 60 pages at the end containing problems tailor-made for the two books.

I’m also working on topological insulators. A topological insulator is a strange beast in which current can flow only on the surface, but not through the interior, or what we call the bulk. (See the article by Xiao-Liang Qi and Shou-Cheng Zhang, Physics Today, January 2010, page 33 .) So you cannot stand on one to change a light bulb. What makes them very attractive to a theorist is that if you chop up the bulk, the new surface you create will carry current. The topology guarantees that. It was again love at first sight.

PT: What are you reading?

SHANKAR: I just came back from a visit to the Niels Bohr Institute, where I got to see their archives. They asked if I wanted to see the original correspondence between [Werner] Heisenberg and Bohr and Einstein, and I said, “You bet I want to see it!” The history of science is very interesting to me because it’s got so many lessons. You realize that many discoveries were not done in a straightforward way; there were a lot of false starts. And very often people who made contributions were not recognized for it in their lifetimes. So if you ever feel that your work is not being given enough credit, you can look at history and find people who are much better than you who got ignored!

The rest of the time, I like to read humorous stuff like P. G. Wodehouse . I’m trying to get my family into it, but I think people who grew up in the Commonwealth or in India are far more addicted to Wodehouse’s style of writing.