In
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...
, ultraviolet completion, or UV completion, of a
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
is the passing from a lower energy
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
to a more general quantum field theory above a threshold value known as the
cutoff. In particular, the more general high energy theory must be well-defined at arbitrarily high energies.
The word "ultraviolet" in this so-called "ultraviolet regime" is only figurative, and refers to energies much higher than
ultraviolet light
Ultraviolet radiation, also known as simply UV, is electromagnetic radiation of wavelengths of 10–400 nanometers, shorter than that of visible light, but longer than X-rays. UV radiation is present in sunlight and constitutes about 10% of th ...
''per se''. Rather, by analogy to the relationship between ultraviolet and visible light, it refers to energies higher than (and wavelengths shorter than) those "visible" to laboratory experiment.
The ultraviolet theory must be
renormalizable
Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that is used to treat infinities arising in calculated quantities by altering values of the ...
;
it can have no
Landau pole
In physics, the Landau pole (or the Moscow zero, or the Landau ghost) is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite. Such a possibility was pointed out by the ph ...
s; and most typically, it enjoys
asymptotic freedom
In quantum field theory, asymptotic freedom is a property of some gauge theory, gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases. (A ...
in the case that it is a quantum field theory (or at least has a nontrivial
fixed point). However, it may also be a background of
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
whose ultraviolet behavior is at least as good as that of renormalizable quantum field theories.
Besides these two known examples (QFT and string theory), it could be a completely different theory than string theory that behaves well at very high energies.
There is an analogous phrase "infrared completion", which applies to length scales longer than those "visible" to normal experiment, particularly
cosmology
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe, the cosmos. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', with the meaning of "a speaking of the wo ...
distances.
See also
*
Ultraviolet divergence
*
Fermi's interaction
In particle physics, Fermi's interaction (also the Fermi theory of beta decay or the Fermi four-fermion interaction) is an explanation of the beta decay, proposed by Enrico Fermi in 1933. The theory posits four fermions directly interacting ...
*
Quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
*
String theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
References
Quantum field theory
Renormalization group
{{quantum-stub