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

${{ℒ}}_D=\overline{\psi }(i{\gamma }^{\mu }{\partial }_{\mu }-m)\psi$

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

${ℒ}\to \overline{{ℒ}}=e^{-i\theta }\overline{\psi }(i{\gamma }^{\mu }{\partial }_{\mu }-m)e^{i\theta }\psi =e^{-i\theta }{e}^{i\theta }\overline{\psi }(i{\gamma }^{\mu }{\partial }_{\mu }-m)\psi ={ℒ}$

See also

• Field
• Global spacetime structure
• Local spacetime structure