Changes

==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: [http://www.wikipedia.org/wiki/15th_Century 15th century]

*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''

==Description==

==Description==

In [http://en.wikipedia.org/wiki/Particle_physics particle physics], dimensional '''transmutation''' is a [[physical]] [[mechanism]] that [[transforms]] a [http://en.wikipedia.org/wiki/Dimensionless dimensionless] [[parameter]] into a [http://en.wikipedia.org/wiki/Dimensionful dimensionful] parameter.

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 [http://en.wikipedia.org/wiki/Field_theory field theory] such as [http://en.wikipedia.org/wiki/Gauge_theory gauge theory] in four-dimensional [[spacetime]], the [http://en.wikipedia.org/wiki/Coupling_constant coupling constant] is a dimensionless constant. However, logarithmic divergences in [http://en.wikipedia.org/wiki/One-loop_diagram one-loop diagrams] imply that this "constant" actually depends on the typical [http://en.wikipedia.org/wiki/Energy_scale energy scale] of the [[processes]] under [[considerations]]. The "running" is determined by the [http://en.wikipedia.org/wiki/Beta-function beta-function] and [http://en.wikipedia.org/wiki/Renormalization_group renormalization group].

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 [http://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.

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 [http://en.wikipedia.org/wiki/Conformal_symmetry conformal symmetry] of the classical theory is anomalously broken, thereby setting up a mass scale. See [http://en.wikipedia.org/wiki/Conformal_anomaly conformal anomaly].

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]]