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 natural phenomena. This is in contrast to experimental physics, which uses experimen ...
, ultraviolet completion, or UV completion, of a
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
is the passing from a lower energy
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
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 ''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, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering va ...
; 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 phy ...
s; and most typically, it enjoys
asymptotic freedom
In quantum field theory, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases.
Asymptotic fre ...
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 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 term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
distances.
See also
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Ultraviolet divergence
In physics, an ultraviolet divergence or UV divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with unbounded energy, or, equivalently, because of physical phenomena at inf ...
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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 ...
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Quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qu ...
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String theory
Quantum field theory
Renormalization group
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