Thursday, January 16, 2014

Quantum Field Theory - the big picture

Taken a first course in Quantum Theory and now interested in moving on to Quantum Field Theory?

Every QFT book you were ever recommended hits you like a suddenly-faced vertical cliff face after a no-more-than-vigorous scramble through those non-relativistic woods. You're used to solving the Schrödinger equation to: model the hydrogen atom; understand molecular binding forces; and chart the motion of (slow) particles in potential fields. Suddenly all that's swept away: you have weird new replacements for Schrödinger - the Klein-Gordon, Dirac and Proca equations .. and then jarringly you're into the alien landscape of Feynman diagrams, propagators and highly convoluted integrals.

Nowhere is the big picture ever explained. How does it all fit together?

At last a book which feels your pain:  "Student Friendly Quantum Field Theory - Basic Principles and Quantum Electrodynamics".
"With regard to phenomena, I recall wondering, as a student, why some of the fundamental things I studied in NRQM (non-relativistic quantum mechanics) seemed to disappear in QFT. One of these was bound state phenomena, such as the hydrogen atom. None of the introductory QFT texts I looked at even mentioned, let alone treated, it. It turns out that QFT can, indeed, handle bound states, but elementary courses typically don’t go there. Neither will we, as time is precious, and other areas of study will turn out to be more fruitful. Those other areas comprise scattering (including inelastic scattering where particles transmute types), deducing particular experimental results, and vacuum energy.

"I also once wondered why spherical solutions to the wave equations are not studied, as they play a big role in NRQM, in both scattering and bound state calculations. It turns out that scattering calculations in QFT can be obtained to high accuracy with the simpler plane wave solutions. So, for most applications in QFT, they suffice.

"Wave packets, as well, can seem nowhere to be found in QFT. Like the other things mentioned, they too can be incorporated into the theory, but simple sinusoids (of complex numbers) serve us well in almost all applications. So, wave packets, too, are generally ignored in introductory (and most advanced) courses.

Wave function collapse, a topic of focus in NRQM, is generally not a topic of focus in QFT texts. It does, however, play a key, commonly hidden role, which is discussed herein in Sects. 7.4.3 and 7.4.4, pgs. 196-197. "
And here is how the book begins - from chapter 1 (PDF):
"Before starting on any journey, thoughtful people study a map of where they will be going. This allows them to maintain their bearings as they progress, and not get lost en route. This chapter is like such a map, a schematic overview of the terrain of quantum field theory (QFT) without the complication of details. You, the student, can get a feeling for the theory, and be somewhat at home with it, even before delving into the “nitty-gritty” mathematics. Hopefully, this will allow you to keep sight of the “big picture”, and minimize confusion, as you make your way, step-by-step, through this book."

Best of all, the first three chapters (and a few more) are free and online (available here).

Thanks, Robert D. Klauber!