Quantum field theory

                       In theoretical physics, quantum field theory (QFT) is a theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics, by treating a particle as an excited state of an underlying physical field. These excited states are called field quanta. For example,quantum electrodynamics (QED) has one electron field and one photon field, quantum chromodynamics (QCD) has one field for each type of quark, and in condensed matter there is an atomic displacement field that gives rise to phonon particles.

In QFT, interactions between particles in quantum mechanics are represented by interaction terms between the underlying fields. QFT interaction terms are similar in spirit to those between electric and magnetic fields in Maxwell's equations. However unlike the classical fields of Maxwell's theory, fields in QFT generally exist in quantum superpositions of states and obey the laws of quantum mechanics.

Quantum mechanical systems have a fixed number of particles, with each particle having a small number of degrees of freedom. In contrast, the excited states of a QFT can represent any number of particles. This makes quantum field theories especially useful for describing systems where the particle count/number may change over time.

Because the fields are continuous quantities over space, there exist excited states with arbitrarily large numbers of particles in them, giving QFT systems an effectively infinite number of degrees of freedom. Infinite degrees of freedom can easily lead to divergences of calculated quantities (i.e., the quantities become infinite) in a straightforward approach to QFT calculations. Techniques such as renormalization of QFT parameters and discretization of spacetime, as in lattice QCD, are used to avoid such infinities and to yield physically meaningful results.

Most theories in modern particle physics are formulated as relativistic quantum field theories, such as QED, QCD, and the Standard Model. In QED the quantum field-theoretic description of the electromagnetic field approximately reproduces Maxwell's theory of electrodynamics in the low-energy limit, with small non-linear corrections to the Maxwell equations being required due to virtual electron–positron pairs.

In the perturbative approach to quantum field theory, the full field interaction terms are approximated as a perturbative expansion in the number of particles involved. Each term in the expansion can be thought of as forces between particles being mediated by other particles. In QED, the electromagnetic force between two electrons is caused by an exchange of photons. Similarly, intermediate vector bosons mediate the weak force and gluons mediate the strong force in QCD. The notion of a force-mediating particle comes from perturbation theory, and does not make sense in the context of non-perturbative approaches to QFT, such as with bound states.

The gravitational field and the electromagnetic field are the only two fundamental fields in nature that have infinite range and a corresponding classical low-energy limit, which greatly diminishes and hides their "particle-like" excitations. Albert Einstein, in 1905, attributed "particle-like" and discrete exchanges of momenta and energy, characteristic of "field quanta", to the electromagnetic field. Originally, his principal motivation was to explain the thermodynamics of radiation. Although the photoelectric effect and Compton scattering strongly suggest the existence of the photon, it is now understood that they can be explained without invoking a quantum electromagnetic field; therefore, a more definitive proof of the quantum nature of radiation is now taken up into modern quantum opticsas in the antibunching effect. The word "photon" was coined in 1926 by physical chemist Gilbert Newton Lewis (see also the articles photon antibunching and laser).

There is currently no complete quantum theory of the remaining fundamental force, gravity. Many of the proposed theories to describe gravity as a QFT postulate the existence of a graviton particle that mediates the gravitational force. Presumably, the as yet unknown correct quantum field-theoretic treatment of the gravitational field will behave like Einstein's general theory of relativity in the low-energy limit. Quantum field theory of the fundamental forces itself has been postulated to be the low-energy effective field theory limit of a more fundamental theory such as superstring theory.