Introduction to Path Integral Methods

Path integrals were introduced by Feynman as an alternative formulation to the conventional hamiltonian approach used in quantum mechanics. The quantum many-body problem can also be formulated in an alternative way without using non-commuting operators (as we have been doing up to here). The partition function, correlation functions and Green functions can be obtained in terms of path integrals. This is in close analogy with classical statistical mechanics. The quantum problem in d-dimensions can be formulated as a classical system with dimensions, \(d+1\) . Hence, the concepts of critical phenomena scaling and renormalization group of classical systems can be applied to quantum systems.