Daily Archives: May 12, 2008

Review: ‘t Hooft’s The Conceptual Basis of Quantum Field Theory

I should be preparing for my 10 minute lecture on classification of hadrons at the American Physical Society’s Northwest meeting on Saturday, but instead I am reading Gerard ‘t Hooft’s beautiful introduction to quantum field theory, The Conceptual Basis of Quantum Field Theory. I like the approach of this book because it concentrates on what I think of as the heart of quantum field theory, Feynman diagrams.

The author begins with classical field theory, but unlike most he defines the solutions to classical field theory with Feynman diagrams! The difference with the quantum theory is that there are no loops; he calls the loops the “quantum corrections” to the classical theory. So all the diagrams are tree diagrams looking something like this:
Tree type Feynman diagram
In the above, the points each correspond to a single point in spacetime. These points are labeled x_j . The G_{49} in the above is a propagator, the Green’s function. Each of the legs carries one of these. The g_{jkl} and \lambda{jklm} are included for the 3-point and 4-point vertices. They are coupling constants. Uh, I’ve been sloppy in the above, please refer to the ‘t Hooft paper for details.
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