ABSTRACT

The path integral introduced in chapter 12 is a representation of the 2-point Green's function or propagator of a quantum mechanical point particle. For propagation from (io, to) to (IA, the path integral viewpoint is a sum over all possible paths or world-lines of the particle starting at (so, to) and ending at (i,t). The contribution of each path to the sum is weighted by the exponential of the classical action evaluated on the particular world-line. If interactions are included, then the possible paths or world-lines to be summed over involve loops and vertices. For example, the perturbative evaluation of the path integral for a particle with cubic self-interaction is represented diagrammatically in figure 21.1(a).