3.5 Quantum Field Theory
Quantum Field Theory combines classical fields, Special Relativity, and Quantum Mechanics in one theoretical framework for constructing quantum mechanical models of subatomic particles, as well as quasi-particles in condensed matter physics. The theory allows infinite numbers of particles, but it predicts how many and with which probabilities or numbers they should exist. When developed further, the theory often contradicts observation, but its creation and annihilation operators can be empirically tied down or renormalized.
Since it was able to combine Special Relativity with Quantum Mechanics, Quantum Field Theory was first believed to be fundamental, but due to its continued failures in quantizing General Relativity, as we shall discuss further in section 5.15, it is only a very good low-energy approximation, or an effective field theory, to some yet undiscovered fundamental theory. The essence of the problem is because it is impossible to quantize space-time itself without supposing some background space in which it is quantized. The Duality of Time seems to be the only way out of this riddle, because it produces a dynamic and self-contained space-time, which will be even extremely easier than the current approaches, such as Strings Theory and Loop Quantum Gravity, because the resulting genuinely-complex time-time geometry is Euclidean and it is intrinsically granular, as we shall discuss this further in chapter V.
Quantum Field Theory treats particles as excited states, or field quanta, of the underlying field, and the interactions among these particles are described by interaction terms among the corresponding underlying quantum fields. These interactions are conveniently visualized by Feynman diagrams, described further in section 5.8.
As Richard Hammond described the conceptual difference between Quantum Mechanics and Quantum Field Theory: “Sometimes we distinguish between Quantum Mechanics (QM) and Quantum Field Theory (QFT). QM refers to a system in which the number of particles is fixed, and the fields (such as the electromechanical field) are continuous classical entities. Quantum Field Theory ... goes a step further and allows for the creation and annihilation of particles.” Hammond (2008)