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A global symmetry is a symmetry that holds for all points in the spacetime under consideration, as opposed to a local symmetry that only holds for an open subset of points.
Most physical theories are described by Lagrangians which are invariant under certain transformations, when the transformations performed at different space-time points are linearly related—they have global symmetries.
In quantum field theory, for example, a global symmetry is any symmetry of a model which is not a gauge symmetry. A gauge symmetry is a local symmetry which only allows us to predict the future evolution of a state given its current state up to a gauge transformation. So, a global symmetry is any symmetry, which acting upon any state, never acts to leave the current state invariant but yet changes the future or past state simultaneously.
See also
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