Conceptual Foundations

In this chapter we will discuss some preliminary philosophical points, dealing with what should be required of the definition of a physical theory in the quantum domain. We will also introduce the most basic foundational objects of the mathematical structure of the theory as it is presented in this book, that is, we will discuss the basic nature of the lattice and introduce the notion of fields defined on it, as well as the notion of functionals of these fields. Special attention will be paid to the notion of the lattice as a representation of space-time, in particular with respect to its geometrical aspects.

The somewhat philosophical points which we will discuss in the first section are nevertheless important to guide the analysis of the mathematical structure of the physical theory, dealing with quantum fields, to be discussed in the other chapters. Although these points are not exactly physical principles, their discussion here is not idle, because they will play a crucial role when the time comes to make some fundamental choices about the mathematical structure of the physical theory, as will be discussed in the last chapter of this book.

The first section is not needed for the understanding of many of the detailed technical aspects presented in the other chapters, except for the discussion in the last chapter, and could be skipped without trouble on a first reading.



Subsections