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 $U(1)=e^{iq\theta}$ (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 wavefunction changes as $\psi\rightarrow e^{iq\theta}\psi$ and $\bar{\psi}\rightarrow e^{-iq\theta}\bar{\psi}$ and so clearly:

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

See also

• Field (physics)
• Global spacetime structure
• Local spacetime structure