Quantum field theory

Quantum field theory is the framework that combines quantum mechanics with special relativity by describing nature in terms of fields that fill all of space, with particles arising as localized excitations, or quanta, of those fields. It is the language of modern particle physics and the basis of the Standard Model, which describes the known elementary particles and three of the four fundamental forces.

#From particles to fields

Ordinary quantum mechanics treats a fixed number of particles moving in time, which is inadequate when particles are created and destroyed, as happens at high energies where mass and energy interconvert. Quantum field theory resolves this by making the field the fundamental object. Each type of particle corresponds to a field: the electron field, the photon field, the quark fields, and so on. A particle is a quantum of excitation of its field, and interactions create and annihilate these quanta. This viewpoint recasts wave-particle duality, since the wave is the field and the particle is its quantum.

#Quantum electrodynamics

The first fully successful quantum field theory was quantum electrodynamics, or QED, which describes the interaction of charged particles with the electromagnetic field. In the late 1940s Sin-Itiro Tomonaga, Julian Schwinger, and Richard Feynman independently developed consistent methods for calculating its predictions, taming the infinities that had plagued earlier attempts through a procedure called renormalization. Richard Feynman introduced the diagram technique that made such calculations tractable, and the three shared the 1965 Nobel Prize (Nobel Foundation 1965). QED predicts quantities such as the magnetic moment of the electron in agreement with experiment to more than ten significant figures, making it among the most precisely verified theories in physics.

#The Standard Model

Extending the same principles to the other forces produced the Standard Model of particle physics. It combines:

• quantum electrodynamics for the electromagnetic force,
• quantum chromodynamics, or QCD, for the strong force that binds quarks into protons and neutrons,
• and the electroweak theory, which unifies electromagnetism with the weak force responsible for certain radioactive decays.

The Standard Model classifies the known quarks and leptons and the force-carrying particles, and it predicted the Higgs boson, whose discovery at CERN in 2012 completed the framework (CERN). The theory has withstood decades of experimental scrutiny at particle accelerators.

#How it works

Calculations in quantum field theory often proceed by perturbation theory, expressing a process as a sum over increasingly complex Feynman diagrams, each representing a way particles can interact by exchanging quanta. Renormalization organizes this expansion so that measurable quantities come out finite. For the strong force at low energies the interactions are too large for this expansion, and other methods such as lattice gauge theory, which simulates the theory on a discretized grid, are used instead (Stanford Encyclopedia of Philosophy).

#Limitations

The Standard Model does not include gravity, which is described separately by general relativity, and combining the two into a quantum theory of gravity remains unsolved. It also does not account for dark matter, dark energy, or the observed masses of neutrinos, and it contains many parameters that must be fixed by experiment rather than derived. These gaps mark the frontier of research beyond the Standard Model.

#Significance

Quantum field theory is the deepest tested description of matter and its interactions at the smallest scales. It unifies the quantum and relativistic pictures, explains the existence and properties of elementary particles, and provides the conceptual foundation on which searches for new physics are built.