Quantum field theory (QFT) is derived from quantum mechanics. It can be seen as an extension or generalization of quantum mechanics to systems with an infinite number of degrees of freedom, such as fields.
Quantum mechanics, developed in the early 20th century, describes the behavior of particles at the microscopic scale, where the laws of classical physics break down. It introduces concepts like wave-particle duality, superposition, and uncertainty, providing a framework for understanding the probabilistic nature of particle interactions and measurements.
Quantum field theory, on the other hand, was developed later as a theoretical framework that combines quantum mechanics with special relativity to describe the behavior of fields and particles in a consistent manner. It treats particles as excitations of underlying fields that pervade space and time.
The development of QFT was motivated by the need to reconcile quantum mechanics with special relativity, which describes the behavior of objects moving at high speeds. Classical field theories, which were used to describe phenomena like electromagnetism, had to be quantized to incorporate the principles of quantum mechanics. This led to the formulation of quantum field theories, such as quantum electrodynamics (QED), which describe the behavior of electrons, photons, and electromagnetic interactions.
So, while quantum mechanics serves as the foundation and framework for understanding the behavior of individual particles, quantum field theory extends this understanding to systems involving fields and interactions among particles. Quantum field theory is a more comprehensive and mathematically sophisticated framework that encompasses and generalizes the principles of quantum mechanics.