The Principles of Quantum Theory, Dirac’s Equation, and the Architecture of Quantum Field Theory

Abstract

This chapter considers the role of the fundamental principles of quantum theory and principle thinking in quantum field theory, beginning with quantum electrodynamics. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory. Dirac’s work, in particular his derivation of his relativistic equation of the electron by combining the principles of relativity and quantum theory, is the main focus of this chapter, in parallel with Heisenberg’s work as the main focus in the discussion of quantum mechanics in Chap. 2. Heisenberg’s work, especially his paper introducing quantum mechanics, which Dirac studied very carefully, was a major influence on Dirac’s thinking throughout, I would argue, all of his work. This influence, however, does not diminish the originality and creativity of Dirac’s thinking, which, ultimately, led him to the discovery of his equation for the relativistic electron and antimatter, one of the greatest discoveries of fundamental physics. After a general introduction given in Sect. 6.1, Sect. 6.2 addresses Dirac’s discovery of his equation. It argues, along the lines of the argument developed in Chap. 2 in considering Heisenberg’s work, that Dirac’s discovery was that of a mathematical machinery, technology, responding to and, in some key respects, specifically as concerns the role of antimatter, anticipating the architecture of high-energy quantum phenomena, as manifested in the experimental technology that defines them. Although not a quantum field theory or even quite quantum electrodynamics, Dirac’s theory of the electron, based in his equation, provided some of the key physical, mathematical, and epistemological ingredients of quantum electrodynamics or quantum field theory as a viable nonrealist theory, to be considered here in terms of a particular concept of quantum field. Dirac’s equation, which expressly considered electrons as particles, was not a field equation, but given its essentially quantum-field-theoretical nature, it would also be difficult to see it merely in terms of relativistic quantum mechanics of particles, as some suggest. Sec. 6.3 addresses the architecture of quantum field theory, as grounded, in addition to the QD and QP/QS principles, which are, just as in quantum mechanics, primary, in the combination of the RWR principle and the particle-transformation, PT, principle. The PT principle emerged as a result of Dirac’s discovery of antimatter, an unintended consequence of his equation. New concepts of both “elementary particle” and “quantum field” are, I argue, required by the combination of both principles, and I shall suggest such concepts here. These concepts allow one to pose and relate the questions “What is a quantum field?” and “What is an elementary particle?” in a new way, even if not answer them. Sec. 6.4 discusses the role of renormalization, and comments on the future of quantum theory and fundamental physics given the current state of quantum field theory.