ABSTRACT
The main purpose of this book is to introduce the reader to the characteristic features of quantum systems with very large or, in the limit infinitely large number of degrees of freedom. Such systems are called quantum fields. As it will be shown below, there is a transparent analogy between the Euclidean form of quantum mechanics and statistical physics - for reason we discuss statistical properties of the fields as well. In this chapter we consider some simple examples of physical fields and related subjects such as the variational principle and quantization rules. There exist two main recipes of quantization: canonical formalism and PI formalism. We shall discuss both, but use mainly the latter in the following chapters. As a simple example we shall consider small field fluctuations near a minimum of the field energy. In the language of quantum mechanics, it will give excitations above the ground state. As it will be shown below, these excitations look like particles.
