In this first chapter of Part II, we introduce the functional-integral formalism that we use throughout the rest of the book to determine the equilibrium properties of a quantum fluid. Today, functional integrals are the preferred tool of researchers working on quantum many-body problems, in particular in condensed-matter physics and high-energy physics. Although this formulation of quantum field theory is of course fully equivalent to the operator formulation developed in the previous chapter, it is in practice more flexible to arrive at systematic approximation schemes and often also leads to a much simpler derivation of exact results. In this chapter, we derive the functional formulation of quantum field theory exactly along the same lines as we derived the path-integral approach to quantum mechanics in Chap. 5. To familiarize ourselves with this new method, we then discuss in detail the ideal quantum gases. The deep and fundamentally different consequences of interactions are then the topic of the rest of the book.
KeywordsPartition Function Coherent State Contour Integration Functional Integral Imaginary Time
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