Quantum field theory

Quantum field theory (QFT) is a framework in theoretical physics that merges classical field theory, special relativity, and quantum mechanics. It provides the foundation for modeling subatomic particles in particle physics and quasiparticles in condensed matter physics, and it underpins the Standard Model of particle physics.

The development of QFT spanned much of the 20th century, beginning in the 1920s with efforts to describe interactions between light and electrons, which led to the first QFT—quantum electrodynamics. Soon after, calculations in perturbative approaches produced persistent infinities, a problem solved in the 1950s through the invention of renormalization. A later obstacle arose when QFT seemed unable to account for weak and strong interactions, prompting some physicists to consider abandoning field theory entirely. The rise of gauge theory and the completion of the Standard Model in the 1970s revived the field.

QFT builds on three earlier theories. The first successful classical field theory emerged from Newton’s law of universal gravitation, though Newton himself described gravity as instantaneous action at a distance. In correspondence, he called such action inconceivable without some mediating non-material substance. In the 18th century, mathematicians introduced fields—numerical quantities assigned to every point in space—to describe gravity, but this was seen as a mere trick. Fields gained physical reality in the 19th century with electromagnetism. Michael Faraday coined the term "field" in 1845, treating fields as properties of space with physical effects, and argued against action at a distance, proposing interactions occur via space-filling lines of force. James Clerk Maxwell completed classical electromagnetism in 1864 with equations linking electric and magnetic fields, electric current, and charge. These equations predicted electromagnetic waves traveling at the speed of light, refuting action at a distance.

Classical electromagnetism could not explain atomic spectral lines or blackbody radiation. Max Planck’s study of blackbody radiation launched quantum mechanics: he treated atoms as tiny oscillators whose energies take only discrete values—quantum harmonic oscillators—a process called quantization. In 1905, Albert Einstein explained the photoelectric effect by proposing light consists of discrete energy packets called photons, showing electromagnetic radiation behaves as both waves and particles. Niels Bohr’s 1913 atomic model introduced discrete electron energies, another quantization example, explaining spectral lines. In 1924, Louis de Broglie proposed wave–particle duality for microscopic particles. These ideas coalesced into quantum mechanics between 1925 and 1926, with contributions from Planck, de Broglie, Heisenberg, Born, Schrödinger, Dirac, and Pauli.

Also in 1905, Einstein published special relativity, built on Maxwell’s electromagnetism. It introduced Lorentz transformations, which change how time and space coordinates shift with observer velocity, blurring the distinction between time and space. Physical laws were required to be invariant under these transformations for observers at different velocities.

Two problems remained. The Schrödinger equation explained stimulated emission—where an electron emits a photon under an external field—but could not explain spontaneous emission, where an electron emits a photon without an external field.