by

Ciro Santilli (@cirosantilli, 36)

Local symmetry

Local symmetries appear to be a synonym to internal symmetry, see description at: Section "Internal and spacetime symmetries".

As mentioned at Quote , local symmetries map to forces in the Standard Model.

Appears to be a synonym for: gauge symmetry.

A local symmetry is a transformation that you apply a different transformation for each point, instead of a single transformation for every point.

TODO what's the point of a local symmetry?

Bibliography:

lecture 3
physics.stackexchange.com/questions/48188/local-and-global-symmetries
www.physics.rutgers.edu/grad/618/lects/localsym.pdf by Joel Shapiro gives one nice high level intuitive idea:
In relativistic physics, global objects are awkward because the finite velocity with which effects can propagate is expressed naturally in terms of local objects. For this reason high energy physics is expressed in terms of a field theory.
Quora:

Table of contents
- Local symmetries of the Lagrangian imply conserved currents Local symmetry

Local symmetries of the Lagrangian imply conserved currents

 0  0 

TODO. I think this is the key point. Notably,

U (1)

symmetry implies charge conservation.

More precisely, each generator of the corresponding Lie algebra leads to one separate conserved current, such that a single symmetry can lead to multiple conserved currents.

This is basically the local symmetry version of Noether's theorem.

Then to maintain charge conservation, we have to maintain local symmetry, which in turn means we have to add a gauge field as shown at Video "Deriving the qED Lagrangian by Dietterich Labs (2018)".

Forces can then be seen as kind of a side effect of this.

Bibliography:

photonics101.com/relativistic-electrodynamics/gauge-invariance-action-charge-conservation#show-solution has a good explanation of the Gauge transformation. TODO how does that relate to $U (1)$ symmetry?
physics.stackexchange.com/questions/57901/noether-theorem-gauge-symmetry-and-conservation-of-charge

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