Local symmetries appear to be a synonym to internal symmetry, see description at: Section "Internal and spacetime symmetries".
A local symmetry is a transformation that you apply a different transformation for each point, instead of a single transformation for every point.
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:
- Quora:
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)".
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 symmetry?
- physics.stackexchange.com/questions/57901/noether-theorem-gauge-symmetry-and-conservation-of-charge
Articles by others on the same topic
Continuous symmetry refers to a type of symmetry that can change smoothly over a range of values, rather than being limited to discrete, specific configurations. In mathematical terms, a system exhibits continuous symmetry if there is a continuous group of transformations (often associated with a Lie group) that leave the system invariant. For example, consider the rotation of a circle.