Friday, September 15, 2006

About my book

I spent a few months rewriting my book Relativistic Quantum Dynamics. and now I have the 2nd edition out. It is much much better than the 1st edition. One important change is that I separated the book into 2 parts. The first part is largely the traditional theory starting from the principle of relativity and ending with the renormalization in QED. The second part has all the new stuff. I analyze the weak points of QED and show how to fix them. I also spent a lot of efforts to make the book more readable, to correct typos and unavoidable errors (signs, missing factors, etc.) in equations. Comments are appreciated.

Which is the most remarkable and under-appreciated paper about QFT?

Take a look at this paper:

Hideji Kita, A Non-Trivial Example of a Relativistic Quantum Theory of Particles without Divergence Difficulties Prog. Theor. Phys. 35 (1965) 934.

Kita builds a fully relativistic theory of interacting particles without even mentioning quantum fields. This theory doesn't have self-interactions and doesn't require renormalization. Both the Hamiltonian and the boost operator are constructed explicitly. They can be used to calculate the time evolution and boost (Lorentz) transformations of observables to the moving reference frame.

He also translates his theory in the language of quantum fields and explicitly shows how the Haag's theorem works. The "interacting quantum field" does not transform covariantly under boost transformations. (Who cares?)

Unfortunately, this work didn't have any impact on the development of QFT. Now it seems to be completely forgotten.

Kita also had a few follow-up papers in Prog. Theor. Phys. in 1960's and 70's. They are real treats!