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 q θ (for θ a constant - making it a global transformation) group on the Dirac Lagrangian:

Under this transformation the wavefunction changes as ψ → e i q θ ψ and ψ ¯ → e − i q θ ψ ¯ and so: