Difference between revisions of "Transmutation"
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==Origin== | ==Origin== | ||
[https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English], from [[Latin]] transmutare, from trans- + mutare to [[change]] — more at mutable | [https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English], from [[Latin]] transmutare, from trans- + mutare to [[change]] — more at mutable | ||
| − | *Date: [ | + | *Date: [https://www.wikipedia.org/wiki/15th_Century 15th century] |
==Definitions== | ==Definitions== | ||
*1 : to [[change]] or alter in form, [[appearance]], or nature and especially to a ''higher form'' | *1 : to [[change]] or alter in form, [[appearance]], or nature and especially to a ''higher form'' | ||
| Line 14: | Line 14: | ||
==Description== | ==Description== | ||
| − | In [ | + | In [https://en.wikipedia.org/wiki/Particle_physics particle physics], dimensional '''transmutation''' is a [[physical]] [[mechanism]] that [[transforms]] a [https://en.wikipedia.org/wiki/Dimensionless dimensionless] [[parameter]] into a [https://en.wikipedia.org/wiki/Dimensionful dimensionful] parameter. |
| − | In classical [ | + | In classical [https://en.wikipedia.org/wiki/Field_theory field theory] such as [https://en.wikipedia.org/wiki/Gauge_theory gauge theory] in four-dimensional [[spacetime]], the [https://en.wikipedia.org/wiki/Coupling_constant coupling constant] is a dimensionless constant. However, logarithmic divergences in [https://en.wikipedia.org/wiki/One-loop_diagram one-loop diagrams] imply that this "constant" actually depends on the typical [https://en.wikipedia.org/wiki/Energy_scale energy scale] of the [[processes]] under [[considerations]]. The "running" is determined by the [https://en.wikipedia.org/wiki/Beta-function beta-function] and [https://en.wikipedia.org/wiki/Renormalization_group renormalization group]. |
| − | Consequently, the strength of the [[interaction]] may be described by a dimensionful parameter, namely the energy scale where the interaction strength reaches the [[value]] 1. In the case of [ | + | Consequently, the strength of the [[interaction]] may be described by a dimensionful parameter, namely the energy scale where the interaction strength reaches the [[value]] 1. In the case of [https://en.wikipedia.org/wiki/Quantum_chromodynamics quantum chromodynamics], this energy scale is called the QCD scale and its value 150 MeV replaces the original dimensionless coupling constant. |
| − | This is a fancy way of saying that the [ | + | This is a fancy way of saying that the [https://en.wikipedia.org/wiki/Conformal_symmetry conformal symmetry] of the classical theory is anomalously broken, thereby setting up a mass scale. See [https://en.wikipedia.org/wiki/Conformal_anomaly conformal anomaly]. |
[[Category: Physics]] | [[Category: Physics]] | ||
[[Category: General Reference]] | [[Category: General Reference]] | ||
Latest revision as of 02:44, 13 December 2020
Origin
Middle English, from Latin transmutare, from trans- + mutare to change — more at mutable
- Date: 15th century
Definitions
- 1 : to change or alter in form, appearance, or nature and especially to a higher form
- 2 : to subject (as an element) to transmutation
Description
In particle physics, dimensional transmutation is a physical mechanism that transforms a dimensionless parameter into a dimensionful parameter.
In classical field theory such as gauge theory in four-dimensional spacetime, the coupling constant is a dimensionless constant. However, logarithmic divergences in one-loop diagrams imply that this "constant" actually depends on the typical energy scale of the processes under considerations. The "running" is determined by the beta-function and renormalization group.
Consequently, the strength of the interaction may be described by a dimensionful parameter, namely the energy scale where the interaction strength reaches the value 1. In the case of quantum chromodynamics, this energy scale is called the QCD scale and its value 150 MeV replaces the original dimensionless coupling constant.
This is a fancy way of saying that the conformal symmetry of the classical theory is anomalously broken, thereby setting up a mass scale. See conformal anomaly.
