Introduction to Quantum Field Theory

Quantum Field Theory (QFT) is the framework that unifies quantum mechanics and special relativity, providing a theoretical foundation for describing fundamental particles and their interactions. Unlike quantum mechanics, which describes particles as wavefunctions evolving in time, QFT treats particles as excitations of underlying fields that pervade all of space. This shift in perspective is necessary to accommodate relativistic effects and to describe processes such as particle creation and annihilation, which are not possible in non-relativistic quantum mechanics. The motivation for QFT arises from the limitations of single-particle quantum mechanics when applied to high-energy physics. In relativistic systems, particles can be created and destroyed in interactions, as seen in high-energy collisions and radioactive decays. Traditional quantum mechanics, which treats particles as fixed entities, cannot account for such processes. By formulating particles as field excitations, QFT allows for a consistent description of multi-particle interactions and naturally incorporates the principles of special relativity. At its core, QFT extends the principles of classical field theory to quantum systems. Classical field theories, such as Maxwell’s electrodynamics, describe how physical quantities vary across space and time. In QFT, these fields are quantized, meaning that their excitations correspond to discrete particles. The simplest example is the Klein-Gordon field, which describes spin-zero particles like mesons. The quantization of this field leads to the interpretation of its solutions as particle states, obeying relativistic energy-momentum relations.