CERN Courier July-August 2016 - Luis Àlvarez-Gaumé review:

Path Integrals for Pedestrians

By E. Gozzi, E. Cattaruzza and C. Pagani
Ed. World Scientific

The path integral formulation of quantum mechanics is one the basic tools used to construct quantum field theories, especially gauge-invariant theories. It is the bread and butter of modern field theory.

Feynman’s original formulation developed and extended some of the work of Dirac in the early 1930s, and provided an elegant and insightful solution to a generic Schrödinger equation.

This short book provides a clear, pedagogical and insightful presentation of the subject. The derivations of the basic results are crystal clear, and the applications worked out to be rather original. It includes a nice presentation of the WKB approximation within this context, including the Van Vleck and functional determinant, the connections formulae and the semiclassical propagator.

An interesting innovation in this book is that the authors provide a clear presentation of the path integral formulation of theWigner functions, which are fundamental in the study of quantum statistical mechanics; and, for the first time in an elementary book, the work of Koopman and von Neumann on classical and statistical mechanics.

The book closes with a well selected set of appendices, where some further technical details and clarifications are presented.

Some of the more mathematical details in the basic derivations can be found there, aswell as aspects of operator ordering as seen from the path integral point formulation, the formulation in momentum space, and the use of Grassmann variables, etc.

It will be difficult to find a better and more compact introduction to this fundamental subject.

Luis Álvarez-Gaumé, CERN.