Quantum Field Theory of Point Particles and Strings

Frontiers in Physics

by Brian Hatfield

The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings.Part II emphasizes the quantization of the bosonic string. The treatment is most detailed in the path integral representation where the object of interest, the partition function, is a sum over random surfaces. The relevant mathematics of Riemann surfaces is covered. Superstrings are briefly introduced, and the sum over genus 0 supersurfaces is computed.The emphasis of the book is calculational, and most computations are presented in step-by-step detail. The book is unique in that it develops all three representations of quantum field theory (operator, functional Schr dinger, and path integral) for point particles and strings. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory.

Genres: Physics, Textbooks, Science

756 pages, Paperback

First published January 1, 1992

Reviews

[Alex Nelson · Rating 4 out of 5]

Be careful which edition you use: get the revised second edition!

I found the first edition in a used bookstore for dirt cheap. (I understand now why the first edition was so cheap: it's riddled with typos.)

As I worked through it, I redid every calculation myself (with the book closed, naturally). But I'm a little rusty with some of the math. So when I finished reproducing the calculations, sometimes I got different results.

I was flustered, especially with the calculation to get from eq (2.72) describing a 2-particle state in the second quantized nonrelativistic free field to the Schrodinger equation for a two-body system. Turns out, it's a typo in the first edition!

The second edition fixed it. Plus the second edition avoided the physically incorrect explanation for delta functions appearing in the potential term.

I suppose this will train me to trust my calculations better...

But still, it's the only book which actually talks about the functional Schrodinger equation in great detail. So you should read it. Just read the corrected second edition.

[Viktor · Rating 5 out of 5]

Excellent overview for both topics! I really liked this book. I also recommend for the basic and intermediate topics Lancester's book (Quantum Field Theory for the Gifted Amateur book).