Let’s start with some historical notes and considerations.
Quantum mechanics as a theory was gradually created and formulated during the first two decades of the 20th century. Important milestones include the 1900 quantum hypothesis by Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete “energy elements” such that each of these elements is proportional to the frequency ν with which each of them individually radiate energy, and then the interpretation of the photoelectric effect.
The origins of quantum field theory date to the 1920s and to the problem of creating a quantum theory of the electromagnetic field.
The first coherent and acceptable theory of quantum electrodynamics, which included the electromagnetic field and electrically charged matter as quantum mechanical objects, was created by Paul Dirac in 1927.
A further development for quantum field theory (or QFT) came with the discovery of the Dirac equation, which was originally formulated and interpreted as a single-particle equation similar to the Schrodinger equation, but the Dirac equation additionally satisfies both the Lorentz invariance, i.e. the requirements of special relativity, and the rules of quantum mechanics.
Theoretical formulations and advances took place during the 1940s and 1950s, resulting the introduction of renormalized quantum electrodynamics (or QED).
Quantum chromodynamics (QCD), the theory of the strong interaction between quarks mediated by gluons, was formulated diring the 1960s.
In the 1960s and 1970s it was shown that the weak nuclear force and quantum electrodynamics could be merged into a single electroweak interaction.
The Standard Model of particle physics, the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles, is a paradigm of a quantum field theory for theorists, exhibiting a wide range of physical phenomena.
Quantum field theory is a quantum mechanical theory. In this theory, fields with quantized normal modes of oscillation represent particles. So particles are regarded as excitations of quantum fields filling all of space. Relativistic theories of quantized fields depict the interactions between elementary particles.
In general, quantum field theory is a theoretical framework combining classical field theory, special relativity, and quantum mechanics. It is used to build physical models of subatomic particles (in relation to particle physics) and quasi-particles (in relation to condensed matter physics).
Below is a helpful description and explanation of quantum field theory, taken from the book A Modern Introduction to Quantum Field Theory, by Michele Maggiore:
“Quantum field theory is a synthesis of quantum mechanics and special relativity, and it is one of the great achievements of modern physics. Quantum mechanics, as formulated by Bohr, Heisenberg, Schrodinger, Pauli, Dirac, and many others, is an intrinsically non-relativistic theory. To make it consistent with special relativity, the real problem is not to find a relativistic generalization of the Schrodinger equation. Actually, Schrodinger first found a relativistic equation, that today we call the Klein–Gordon equation. He then discarded it because it gave the wrong fine structure for the hydrogen atom, and he retained only the non-relativistic limit. Wave equations, relativistic or not, cannot account for processes in which the number and the type of particles changes, as in almost all reactions of nuclear and particle physics.[…] Furthermore, relativistic wave equations suffer from a number of pathologies, like negative-energy solutions.
A proper resolution of these difficulties implies a change of viewpoint, from wave equations, where one quantizes a single particle in an external classical potential, to quantum field theory, where one identifies the particles with the modes of a field, and quantizes the field itself. The procedure also goes under the name of second quantization.
The methods of quantum field theory (QFT) have great generality and flexibility and are not restricted to the domain of particle physics. In a sense, field theory is a universal language, and it permeates many branches of modern research. In general, field theory is the correct language whenever we face collective phenomena, involving a large number of degrees of freedom, and this is the underlying reason for its unifying power. For example, in condensed matter the excitations in a solid are quanta of fields, and can be studied with field theoretical methods. An especially interesting example of the unifying power of QFT is given by the phenomenon of superconductivity which, expressed in the field theory language, turns out to be conceptually the same as the Higgs mechanism in particle physics. As another example we can mention that the Feynman path integral, which is a basic tool of modern quantum field theory, provides a formal analogy between field theory and statistical mechanics, which has stimulated very important exchanges between these two areas.”
For additional info and details about these topics, the following links can be viewed or consulted:
Differences between principles of QM and QFT
Knowledge mix 