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 experim ...
, cutoff (AE: cutoff, BE: cut-off) is an arbitrary maximal or minimal value of
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
,
momentum, or
length, used in order that objects with larger or smaller values than these
physical quantities
A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For exam ...
are ignored in some calculation. It is usually represented within a particular
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
or
length scale
In physics, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot af ...
, such as
Planck units.
When used in this context, the traditional terms "
infrared
Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
" and "
ultraviolet
Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm (with a corresponding frequency around 30 PHz) to 400 nm (750 THz), shorter than that of visible light, but longer than X-rays. UV radiation ...
" 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
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
(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
In physics, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot af ...
).
Effect on calculation
A typical use of cutoffs is to prevent
singularities from appearing during calculation. If some quantities are computed as
integral
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along wit ...
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
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the ...
.
See also
*
Infrared fixed point
In physics, an infrared fixed point is a set of coupling constants, or other parameters, that evolve from initial values at very high energies (short distance) to fixed stable values, usually predictable, at low energies (large distance). This usu ...
*
Ultraviolet fixed point
Quantum field theory
Statistical mechanics
Renormalization group
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