Physics:Global symmetry

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 [math]\displaystyle{ U(1)=e^{i\theta} }[/math] (for [math]\displaystyle{ \theta }[/math] a constant - making it a global transformation) group on the Dirac Lagrangian:

[math]\displaystyle{ \mathcal{L}_D = \bar{\psi}\left(i\gamma^\mu \partial_\mu-m\right)\psi }[/math]

Under this transformation the fermionic field changes as [math]\displaystyle{ \psi\rightarrow e^{i\theta}\psi }[/math] and [math]\displaystyle{ \bar{\psi}\rightarrow e^{-i\theta}\bar{\psi} }[/math] and so:

[math]\displaystyle{ \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

• Field
• Global spacetime structure
• Local spacetime structure