Physics Over Formalism

Perhaps one could call it my “style” of doing physics, but I much prefer to understand phenomena in solids without the use of field theoretical techniques and formalism associated with those methods (i.e. Green functions, Imaginary time, Matsubara sums, Feynman diagrams, etc.). While many may consider it a necessity in the modern theoretical landscape, as an experimentalist I feel like I may be better off without the confusion that these methods elicit.

This attitude is undoubtedly in part due to the influence of A.J. Leggett, whose many lectures I have attended, and who presently eschews these methods dogmatically. In the previous years of my graduate studies, I spent innumerable hours trying to gain an understanding of the role that a Green function serves in solid state physics. I can discuss them fluently with theorists, but I never reached the level where the use of Green functions became second nature to me. I can say without reservation, though, that  I did not gain any significant insight from them that I did not already have from more basic methods.

After having made the conscious decision to leave these methods aside, I find myself liberated to some degree. I am able to concentrate on learning the basic physics that occurs in solids without the obfuscating (to me) formalism.

The strange thing I have noticed since “letting go” is that I have been able learn much more. This is so in two senses: (1) I have been able to gain a better understanding of phenomena that is commonly understood through the use of Green functions. The Random Phase Approximation (RPA) is a case in point. (2) Because I spend less time worrying about formalism, I have been able to cover more material.

There are a number of books that have advanced my understanding of solids that have not required the use of field theoretical methods:

  1. Quantum Liquids – Leggett
  2. The Theory of Quantum Liquids – Pines and Nozieres
  3. Electrodynamics of Solids – Dressel and Gruner
  4. Principles of the Theory of Solids – Ziman
  5. Superfluids, Superconductors and Condensates – Annett
  6. Topological Quantum Numbers in Non-Relativistic Physics – Thouless
  7. Introduction to Superconductivity – Tinkham
  8. Density Waves in Solids – Gruner

Comments are encouraged as I’m curious to know other peoples’ opinions on this matter.

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6 responses to “Physics Over Formalism

  1. I am interested in condensed matter physics too. My interest is partly due to the fact that CMP is arbitrary and rich. By rich I mean there are lots of profound physical ideas to explore and understand without depending too much on rigor and using fancy mathematics, formalism, etc. By arbitrary I mean the decision based on physical intuition that what approximation suits a certain problem the best (case in point: Anderson included the U term in his magnetic impurity Hamiltonian which produced lots of physics). I totally agree with you about “physics over formalism”.

    The question is, how do you make it without using field theoretical methods? You mentioned RPA as an example. I myself, first learned RPA’s mean field treatment, then I learned it by the means of Feynman diagrams. I always try to learn various concepts from different perspectives in order to make a vivid physical picture in my mind, therefore I tried to gain some more insight by learning wave function treatment of RPA. I grabbed Madelung’s solid state book and… it was boring. I couldn’t understand anything there and soon gave up.

    My point is sometimes field theory formalism might be helpful for some people so it is not a good idea to be stubborn. I don’t mean you are stubborn because you don’t like field theory. All I want to say is everything might be helpful at some point, so it’s always a good idea to keep options open.

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    • Thanks for your comment. I totally agree, one should have an open mind. Because I don’t use these methods often enough though, they often lead to confusion (at least for me). I think that for the seasoned practitioner, they are very useful.

      Personally, I just think that a whole slew of phenomena in solid state physics can be understood without them. If the methods become necessary for me to understand something I’m working on in the lab, then I will have to take the plunge (again). For now, I will continue without them until I hit an insurmountable block.

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      • That’s true. I didn’t notice that you are an experimentalist, I am more theoretically inclined and this may be the reason why I like field theory more. However, CMP is too beautiful to be thoroughly expressible using just field theory.

        Anyways, thank you for making a blog about this “exciting but little known to the public” discipline.

        Keep up the good work.

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  2. Thanks! I appreciate you saying that.

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  3. Alternatively, condensed matter provides an elementary way to understand field theory!

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