Chapter 4 - Further Applications

Abstract

Publisher Summary This chapter presents the extensions of quantum mechanical path integrals. It discusses natural units, the choice of which is that of length so that all physical quantities are represented in the powers of length. The chapter further illustrates the relationship of the quantum mechanical partition function to the path integral and explains the development of the concept of symmetry in quantum mechanical systems. It illustrates the implications of symmetries for various formulations of the generating functionals. In the chapter, the harmonic oscillator is reformulated in terms of coherent states and a path integral representation of the vacuum persistence amplitude is derived using these coherent states. The chapter discusses the mechanism of the spontaneous breakdown of symmetry for a simple quantum mechanical system and the derivation of effective potential. It also explains the implementation of constraints in the path integral formalism.