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

Under this transformation the wavefunction changes as ${\displaystyle \psi \rightarrow e^{iq\theta }\psi }$ and ${\displaystyle {\bar {\psi }}\rightarrow e^{-iq\theta }{\bar {\psi }}}$ and so:

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