Global symmetry: Difference between revisions

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	Global symmetries require ]s, but not ], in physics.		Global symmetries require ]s, but not ], in physics.

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

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

	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:		Under this transformation the fermionic field changes as <math>\psi\rightarrow e^{i\theta}\psi</math> and <math>\bar{\psi}\rightarrow e^{-i\theta}\bar{\psi}</math><ref>http://www.damtp.cam.ac.uk/user/tong/qft.html</ref> and so:

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

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

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In physics, 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 $U(1)=e^{i\theta }$ (for $\theta$ a constant - making it a global transformation) group on the Dirac Lagrangian:

{\mathcal {L}}_{D}={\bar {\psi }}\left(i\gamma ^{\mu }\partial _{\mu }-m\right)\psi

Under this transformation the fermionic field changes as $\psi \rightarrow e^{i\theta }\psi$ and ${\bar {\psi }}\rightarrow e^{-i\theta }{\bar {\psi }}$ and so:

{\mathcal {L}}\rightarrow {\bar {\mathcal {L}}}=e^{-i\theta }{\bar {\psi }}\left(i\gamma ^{\mu }\partial _{\mu }-m\right)e^{i\theta }\psi =e^{-i\theta }e^{i\theta }{\bar {\psi }}\left(i\gamma ^{\mu }\partial _{\mu }-m\right)\psi ={\mathcal {L}}

Revision as of 10:33, 15 February 2018

See also