A QFT treats particles as excited states of an underlying physical field, so these 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. Edward Witten describes QFT as "by far" the most difficult theory in modern physics.[1]
In QFT, quantum mechanical interactions between particles are described by interaction terms between the corresponding underlying fields. QFT interaction terms are similar in spirit to those between charges with 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 are subject to the laws of quantum mechanics.
Quantum mechanical systems have a fixed number of particles, with each particle having a finite 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, a crucial feature of relativistic dynamics.
Because the fields are continuous quantities over space, there exist excited states with arbitrarily large numbers of particles in them, providing QFT systems with 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). Techniques such as renormalization of QFT parameters or discretization of spacetime, as in lattice QCD, are often used to avoid such infinities so as to yield physically meaningful results.
Most theories in standard particle physics are formulated as relativistic quantum field theories, such as QED, QCD, and the Standard Model. 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 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 optics as in the antibunching effect.[2]
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.
Quantum field theory. Quantum field theory in curved spacetime. In particle physics, quantum field theory in curved spacetime is an extension of standard, Minkowski-space quantum field theory to curved spacetime. A general prediction of this theory is that particles can be created by time-dependent gravitational fields (multigraviton pair production), or by time-independent gravitational fields that contain horizons. Description[edit] Interesting new phenomena occur; owing to the equivalence principle the quantization procedure locally resembles that of normal coordinates where the affine connection at the origin is set to zero and a nonzero Riemann tensor in general once the proper (covariant) formalism is chosen; however, even in flat spacetime quantum field theory, the number of particles is not well-defined locally.
For non-zero cosmological constants, on curved spacetimes quantum fields lose their interpretation as asymptotic particles. Applications[edit] Approximation to quantum gravity[edit] See also[edit] References[edit] Notes[edit] N.D. Geometrodynamics. In theoretical physics, geometrodynamics is an attempt to describe spacetime and associated phenomena completely in terms of geometry. Technically, its goal is to unify the fundamental forces and reformulate general relativity as a configuration space of three-metrics, modulo three-dimensional diffeomorphisms. It was enthusiastically promoted by John Wheeler in the 1960s, and work on it continues in the 21st century. Einstein's geometrodynamics[edit] Wheeler's geometrodynamics[edit] Wheeler wanted to reduce physics to geometry in an even more fundamental way than the ADM reformulation of general relativity with a dynamic geometry whose curvature changes with time.
It attempts to realize three concepts: mass without masscharge without chargefield without field. He wanted to lay the foundation for quantum gravity and unify gravitation with electromagnetism (the strong and weak interactions were not yet sufficiently well understood in 1960 to be included). References[edit] Anderson, E. (2004). Static forces and virtual-particle exchange. The virtual-particle description of static forces is capable of identifying the spatial form of the forces, such as the inverse-square behavior in Newton's law of universal gravitation and in Coulomb's law. It is also able to predict whether the forces are attractive or repulsive for like bodies. As with any physical theory, there are limits to the validity of the virtual particle picture. The virtual-particle formulation is derived from a method known as perturbation theory which is an approximation assuming interactions are not too strong, and was intended for scattering problems, not bound states such as atoms.
For the strong force binding quarks into nucleons at low energies, perturbation theory has never been shown to yield results in accord with experiments,[2] thus, the validity of the "force-mediating particle" picture is questionable. Similarly, for bound states the method fails.[3] In these cases the physical interpretation must be re-examined. Classical forces[edit] is to mass.
Symmetry in quantum mechanics. Notation[edit] Symmetry transformations on the wavefunction in non-relativistic quantum mechanics[edit] Continuous symmetries[edit] Generally, the correspondence between continuous symmetries and conservation laws is given by Noether's theorem. The form of the fundamental quantum operators, for example energy as a partial time derivative and momentum as a spatial gradient, becomes clear when one considers the initial state, then changes one parameter of it slightly.
In what follows, transformations on only one-particle wavefunctions in the form: are considered, where denotes a unitary operator. . Now, the action of changes ψ(r, t) to ψ(r′, t′), so the inverse changes ψ(r′, t′) back to ψ(r, t), so an operator invariant under satisfies: and thus: for any state ψ. Overview of Lie group theory[edit] Following are the key points of group theory relevant to quantum theory, examples are given throughout the article. And all parameters set to zero returns the identity element of the group: .
Where . And. Photon polarization. Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photon eigenstates have either right or left circular polarization. A photon that is in a superposition of eigenstates can have linear, circular, or elliptical polarization. The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well, and forms a fundamental basis for an understanding of more complicated quantum phenomena. Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description.
Polarization of classical electromagnetic waves[edit] Polarization states[edit] Linear polarization[edit] Effect of a polarizer on reflection from mud flats. .
Principles of Quantum field theory. A list of Quantum field theories.