Misplaced Pages

Global symmetry: Difference between revisions

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Browse history interactively← Previous editNext edit →Content deleted Content addedVisualWikitext
Revision as of 21:29, 19 May 2012 editMcoupal (talk | contribs)Extended confirmed users5,863 editsNo edit summary← Previous edit Revision as of 20:03, 25 July 2012 edit undoThaeliosActual (talk | contribs)4 editsNo edit summaryNext edit →
Line 10: Line 10:
Under this transformation the wavefunction changes as <math>\psi\rightarrow e^{iq\theta}\psi</math> and <math>\bar{\psi}\rightarrow e^{-iq\theta}\bar{\psi}</math> and so clearly: Under this transformation the wavefunction changes as <math>\psi\rightarrow e^{iq\theta}\psi</math> and <math>\bar{\psi}\rightarrow e^{-iq\theta}\bar{\psi}</math> and so clearly:


::<math>\mathcal{L}\rightarrow\bar{\mathcal{L}}=e^{-iq\theta}\bar{\psi}\left(i\gamma^\mu \partial_\mu-m\right)e^{iq\theta}\psi=e^{-iq\theta}e^{iq\theta}\bar{\psi}\left(i\gamma^\mu \partial_\mu-m\right)=\mathcal{L}</math> ::<math>\mathcal{L}\rightarrow\bar{\mathcal{L}}=e^{-iq\theta}\bar{\psi}\left(i\gamma^\mu \partial_\mu-m\right)e^{iq\theta}\psi=e^{-iq\theta}e^{iq\theta}\bar{\psi}\left(i\gamma^\mu \partial_\mu-m\right)\psi=\mathcal{L}</math>


==See also== ==See also==

Revision as of 20:03, 25 July 2012

This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.
Find sources: "Global symmetry" – news · newspapers · books · scholar · JSTOR (December 2009) (Learn how and when to remove this message)

A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.

Global symmetries require conservation laws, but not forces, in physics.

An example of a global symmetry is the action of the U ( 1 ) = e i q θ {\displaystyle U(1)=e^{iq\theta }} (for θ {\displaystyle \theta } a constant - making it a global transformation) group on the Dirac Lagrangian:

L D = ψ ¯ ( i γ μ ∂ μ − m ) ψ {\displaystyle {\mathcal {L}}_{D}={\bar {\psi }}\left(i\gamma ^{\mu }\partial _{\mu }-m\right)\psi }

Under this transformation the wavefunction changes as ψ → e i q θ ψ {\displaystyle \psi \rightarrow e^{iq\theta }\psi } and ψ ¯ → e − i q θ ψ ¯ {\displaystyle {\bar {\psi }}\rightarrow e^{-iq\theta }{\bar {\psi }}} and so clearly:

L → L ¯ = e − i q θ ψ ¯ ( i γ μ ∂ μ − m ) e i q θ ψ = e − i q θ e i q θ ψ ¯ ( i γ μ ∂ μ − m ) ψ = L {\displaystyle {\mathcal {L}}\rightarrow {\bar {\mathcal {L}}}=e^{-iq\theta }{\bar {\psi }}\left(i\gamma ^{\mu }\partial _{\mu }-m\right)e^{iq\theta }\psi =e^{-iq\theta }e^{iq\theta }{\bar {\psi }}\left(i\gamma ^{\mu }\partial _{\mu }-m\right)\psi ={\mathcal {L}}}

See also


Stub icon

This physics-related article is a stub. You can help Misplaced Pages by expanding it.

Categories: