Tag Archives: Green Functions

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.