Editing Cutoff (physics)

{{short description|Maximum or minimum values of quantities}}
{{Unreferenced|date=December 2009}}

In [[theoretical physics]], '''cutoff''' (AE: cutoff, BE: cut-off) is an arbitrary maximal or minimal value of [[energy]], [[momentum]], or [[length]], used in order that objects with larger or smaller values than these [[physical quantity|physical quantities]] are ignored in some calculation. It is usually represented within a particular [[energy scale|energy]] or [[length scale]], such as [[Planck units]].

When used in this context, the traditional terms "[[infrared]]" and "[[ultraviolet]]" are not literal references to specific regions of the spectrum, but rather refer by analogy to portions of a calculation for low energies (infrared) and high energies (ultraviolet), respectively.

==Infrared and ultraviolet cutoff==
An '''infrared cutoff''' (long-distance cutoff) is the minimal value of energy – or, equivalently, the maximal [[wavelength]] (usually a very large distance) – that will be taken into account in a calculation, typically an integral.

At the opposite end of the energy scale, an '''ultraviolet cutoff''' is the maximal allowed energy or the shortest allowed distance (usually a very short [[length scale]]).

==Effect on calculation==
A typical use of cutoffs is to prevent [[mathematical singularity|singularities]] from appearing during calculation. If some quantities are computed as [[integral]]s over energy or another physical quantity, these cutoffs determine the limits of integration. The exact physics is reproduced when the appropriate cutoffs are sent to zero or infinity. However, these integrals are often divergent – see [[IR divergence]] and [[UV divergence]] – and a cutoff is needed. The dependence of physical quantities on the chosen cutoffs (especially the ultraviolet cutoffs) is the main focus of the theory of the [[renormalization group]].

==See also==
* [[Infrared fixed point]]
* [[Ultraviolet fixed point]]

==References==
{{reflist}}
[[Category:Quantum field theory]]
[[Category:Statistical mechanics]]
[[Category:Renormalization group]]


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