The standard quantum theory as developed by Niels Bohr, W. Heisenberg, Schrödinger and others in the 1920s is fine for describing the workings of individual particles in isolation and at slow speeds. But to explain their interactions in the real world, we need something more.

The Schrödinger equation, developed by Erwin Schrödinger, is a partial differential equation that governs the wave function of a quantum-mechanical system. It is a foundational equation in quantum mechanics. However, the equation comes with two primary difficulties.

Observationally, the Schrödinger equation could explain the stimulated emission of radiation from atoms, where an electron emits a new photon under the action of an external EM field, but it was unable to explain spontaneous emission...

...where an electron spontaneously decreases in energy and emits a photon even without the action of an external electromagnetic field. Secondly, Theoretically, it could not describe photons and was inconsistent with the principles of special relativity (provided by Einstein).

You can check out my thread on Learning Quantum Mechanics for free 👇

In the late 1920s, Dirac introduced an equation called 'Dirac equation' which turned out to be consistent with the abstract Schrödinger equation and is linear in both time and space derivatives, and so it had a chance to be consistent with relativity. (iγ∂ − m) ψ(x) = 0

Bohr: What are you working on? Dirac: I’m trying to get a relativistic theory of the electron. Bohr: But Klein has already solved that problem. (Conversation at the 1927 Solvay Conference.)

In 1927 Dirac published a paper titled "The quantum theory of the emission and absorption of radiation" where he coined the term quantum electrodynamics (QED), the first quantum field theory, incorporating both quantum mechanics and the theory of special relativity.

Quantum Field Theory (QFT) explains the behavior of atoms and the particles within atoms like electrons and quarks. Physicists rely primarily on mathematical equations to describe how particles act. QFT provides a story of how particles interact.

Lemme keep it this way, the 'conventional' quantum theory suggests that particles can act like both particles and waves. QFT suggests that there are no particles and no waves; just fields. Both "particles" and "waves" are two ways in which we naively interpret quantum fields.

In QFT, “empty space” is actually filled with fields. Each field corresponds to a particular particle. There's one field for each type of particle. So one field for all photons in the universe, one field for all electrons, and so on. And these fields exist everywhere.

We can perceive ripples in a field (analogous to ripples in the water of a pond) as a particle. Ripples in the electromagnetic field, its particles, are called “photons.” Photons bring us light, radio and TV broadcasts, and cell phone calls.

To "extract" a particle from a field, you need to give the field energy. If you give it enough energy, the field will go to a higher energy state. These states are what we interpret as particles.

Some fields require more energy than others in order to create a particle. The amount of energy is proportional to the mass of the associated particle. A Higgs boson is much more massive than an electron. So electrons are easy to create, but Higgs bosons are very hard to create.

In 1928 the English physicist P.A.M. Dirac laid the foundations for QED with his discovery of a wave equation that described the motion and spin of electrons and incorporated both quantum mechanics and the theory of special relativity.

QED was refined and fully developed in the late 1940s by Richard P. Feynman, Julian S. Schwinger, and Shin’ichirō Tomonaga , independently of one another. It rests on the idea that charged particles (e.g., electrons and positrons) interact by emitting and absorbing photons.

The interaction of two charged particles occurs in a series of processes of increasing complexity. In the simplest, only one virtual photon is involved; in a second-order process, there are two; and so forth.

The key components of Feynman's presentation of QED are three basic actions: A photon goes from one place and time to another place and time. An electron goes from one place and time to another place and time. An electron emits or absorbs a photon at a certain place and time.

The processes correspond to all the possible ways in which the particles can interact by the exchange of virtual photons, and each of them can be represented graphically by means of the so-called Feynman diagrams.

In Feynman diagrams: a wavy line for the photon, a straight line for the electron and a junction of two straight lines and a wavy one for a vertex representing emission or absorption of a photon by an electron. These can all be seen in the adjacent diagram.

QFT has been an extremely successful theory and is very widely used to solve many problems and explain several phenomena in modern physics, statistical physics, cosmology and astrophysics, condensed matter physics and many other fields.

Thank you so much for reading. If you enjoyed this thread, do subscribe my newsletter to be a part of my physics community where I share multiple resources, articles and journals of Physics and Mathematics: