Global symmetry

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

ℒD=ψ¯(iγμ∂μ−m)ψ

Under this transformation the fermionic field changes as ψ->eiθψ and ψ¯->e−iθψ¯[1] and so:

ℒ->ℒ¯=e−iθψ¯(iγμ∂μ−m)eiθψ=e−iθeiθψ¯(iγμ∂μ−m)ψ=ℒ

## See also

* Field
* Global spacetime structure
* Local spacetime structure

## References

1. ↑ http://www.damtp.cam.ac.uk/user/tong/qft.html

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