Quantum field theory

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Quantum field theory (QFT) provides a theoretical framework for constructing quantum mechanical models of systems classically represented by an infinite number of degrees of freedom, that is, fields and (in a condensed matter context) many-body systems. It is the natural and quantitative language of particle physics and condensed matter physics. Most theories in modern particle physics, including the Standard Model of elementary particles and their interactions, are formulated as relativistic quantum field theories. Quantum field theories are used in many contexts, and are especially vital in elementary particle physics, where the particle count/number may change over the course of a reaction. They are also used in the description of critical phenomena and quantum phase transitions, such as in the BCS theory of superconductivity.

In perturbative quantum field theory, the forces between particles are mediated by other particles. The electromagnetic force between two electrons is caused by an exchange of photons. Intermediate vector bosons mediate the weak force and gluons mediate the strong force. There is currently no complete quantum theory of the remaining fundamental force, gravity, but many of the proposed theories postulate the existence of a graviton particle that mediates it. These force-carrying particles are virtual particles and, by definition, cannot be detected while carrying the force, because such detection will imply that the force is not being carried. In addition, the notion of "force mediating particle" comes from perturbation theory, and thus does not make sense in a context of bound states.

In QFT, photons are not thought of as "little billiard balls" but are rather viewed as field quanta – necessarily chunked ripples in a field, or "excitations", that "look like" particles. Fermions, like the electron, can also be described as ripples/excitations in a field, where each kind of fermion has its own field. In summary, the classical visualisation of "everything is particles and fields", in quantum field theory, resolves into "everything is particles", which then resolves into "everything is fields". In the end, particles are regarded as excited states of a field (field quanta). 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 it is often claimed that the photoelectric and Compton effects require a quantum description of the EM field, this is now understood to be untrue, and proper proof of the quantum nature of radiation is now taken up into modern quantum optics as in the antibunching effect.^[1] The word "photon" was coined in 1926 by physical chemist Gilbert Newton Lewis (see also the articles photon antibunching and laser).

There are several theories using the QFT framework, such as quantum electrodynamics and quantum chromodynamics. Within a theory, there is one field for each type of particle in that theory, and interaction terms between the fields. For example, QED has one electron field and one photon field; QCD has one field for each type of quark, etc. The interaction terms are similar in spirit to those in Maxwell's equations, being interactions between fields. However unlike Maxwell's theory, QFT fields generally exist in superpositions of states.

In the "low-energy limit", the quantum field-theoretic description of the electromagnetic field, quantum electrodynamics, does not exactly reduce to James Clerk Maxwell's 1864 theory of classical electrodynamics. Small quantum corrections due to virtual electron-positron pairs give rise to small non-linear corrections to the Maxwell equations, although the "classical limit" of quantum electrodynamics has not been as widely explored as that of quantum mechanics.

Presumably, the as yet unknown correct quantum field-theoretic treatment of the gravitational field will become and "look exactly like" Einstein's general theory of relativity in the "low-energy limit", or, more generally, like the Einstein-Yang-Mills-Dirac System. Indeed, quantum field theory itself is possibly the low-energy-effective-field-theory limit of a more fundamental theory such as the highly speculative superstring theory