Path integrals and degrees of freedom in many-body systems and relativistic field theories

The identification of physical degrees of freedom is sometimes obscured in the path-integral formalism, and this makes it difficult to impose some constraints or to do some approximations. I review a number of cases where the difficulty is overcome by deriving the path integral from the operator form of the partition function after such identification has been made. (c) 2005 Pleiades Publishing, Inc.