In this chapter we return to path integrals for a more detailed and advanced treatment. The tools described here are so widely used in so many branches of physics, that it makes sense to include them in a book such as this. This chapter will be different from the earlier ones in that it will try to introduce you to a variety of new topics without giving all the derivations in the same detail as before. It also has a list of references to help you pursue any topic that attracts you. The list is not exhaustive and consists mostly of pedagogical reviews or books. From the references these references contain, you can pursue any given topic in greater depth. All this will facilitate the transition from course work to research.
KeywordsPartition Function Coherent State Vector Potential Path Integral Landau Level
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- S. Coleman, Aspects of Symmetry (Cambridge University Press, New York, 1985). Included here for the article on instantons.Google Scholar
- L. D. Faddeev, in Methods in Field Theory, Les Houches Lectures, 1975 (R. Balian and J. Zinn-Justin, eds.) (North-Holland/World Scientific, Singapore, 1981). Look in particular at the discussion of holomorphic form of the functional integral. i.e., the coherent state integral.Google Scholar
- M. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer Verlag, New York, 1990). For a solid introduction to many aspects of path integrals, especially the semiclasslcal limit.Google Scholar
- J. R. Klauder and B. Skagerstam, eds., Coherent States (World Scientific, Singapore, 1985). Everything you ever wanted to know about coherent states.Google Scholar
- S. Pancharatnam, Ind. Acad. Sci., 44(5), Sec. A, 1958. Reprinted in Shapere and Wilczek (1989) (see below). Discusses the geometric phase in the context of optics.Google Scholar
- R. E. Prange and S. M. Girvin, eds., The Quantum Hall Effect (Springer, New York, 1987). Has many contributed papers by leaders in the field as well as helpful commentaries.Google Scholar
- R. Rajaraman, Instantons and Solitons (North Holland, New York, 1982). Extremely clear discussion of the subject, usually starting with a warmup toy example from elementary quantum mechanics. Very few details are “left to the reader.”Google Scholar
- L. S. Schulman, Techniques and Applications of Path Integrals (Wiley Interscience, New York, 1981). A very readable and clear discussion of functional integrals, and pitfalls and fine points (such as the midpoint prescription for vector potential coupling).Google Scholar
- A. Shapere and F. Wilczek, eds., Geometric Phases in Physics (World Scientific, Singapore, 1989). Collection of all key papers and some very good introductions to each subtopic. Saves countless trips to the library.Google Scholar
- M. Stone. ed., The Quantum Hall Effect (World Scientific, Singapore, 1992). A nice collection of reprints with commentary.Google Scholar
- 't Hooft, Phys. Rev. Lett., 37, 8 (1976).Google Scholar
- F. Wilczek, ed., Fractional Statistics and Anyon Superconductivity (World Scientific, Singapore, 1990). Referenced here for its applications to the Quantum Hall Effect. However, other topics like fractional statistics discussed there should be within your reach after this book.Google Scholar