ABSTRACT

There are two widely used approaches to quantum field theory. The first is based on field operators and the canonical quantisation of these operator fields, and will not be discussed in this book. The second approach, as we shall see in Chapter 4, involves path integrals 1 over classical fields, and it is upon this latter approach that this book relies for its derivations. In this chapter, the idea of path integrals (or functional integrals) will be developed in a very intuitive way without any attempt at mathematical precision or rigour. Instead, the analogy between vectors and functions, and between matrices and differential operators on functions will be exploited extensively. Since very few path integrals can be performed exactly, we shall concentrate on Gaussian path integrals 2 . These are important in their own right, but much more so because they can be used in approximation schemes when the exact path integral is intractable, as we shall see in later chapters.