Functional integral representation of the partition function
Joseph I. Kapusta, Charles Gale
Functional integral representation of the partition functionThe customary approach to nonrelativistic many-body theory is to proceed with the method of second quantization begun in the first chapter.There is another approach, the method of functional integrals, which we shall follow here.Of course, what can be done in one formalism can always be done in another.Nevertheless, functional integrals seem to be the method of choice for most elementary particle theorists these days, and they seem to lend themselves more readily to nonperturbative phenomena such as tunneling, instantons, lattice gauge theory, etc.For gauge theories they are practically indispensable.However, there is a certain amount of formalism that must be developed before we can start to discuss physical applications.In this chapter, we shall derive the functional integral representation of the partition function for interacting relativistic non-gauge field theories.As a check on the formalism, as well as to obtain some feeling for how functional integrals work, we shall then rederive some well-known results on relativistic ideal gases for bosons and fermions.
Cambridge University Press eBooks•Jul 13, 2023•1 citation