Symmetry and Conservation of Charge

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Discussion Overview

The discussion revolves around the relationship between symmetries and conservation laws, specifically focusing on the conservation of charge. Participants explore the nature of gauge symmetries, distinguishing between global and local gauge symmetries, and their implications for conservation laws.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant asserts that conservation laws are linked to underlying symmetries, asking what symmetry corresponds to the conservation of charge.
  • Another participant proposes that the conservation of charge follows from global gauge symmetry.
  • A participant questions the validity of referring to global gauge symmetry, suggesting that "gauge" implies a local symmetry.
  • In response, a participant clarifies that global gauge symmetries are independent of spatial coordinates, while local gauge symmetries depend on them, and reflects on the nature of gauge symmetries in the context of potential fields.
  • Another participant acknowledges the confusion surrounding the terminology, noting that both "local gauge symmetry" and "global gauge symmetry" are accepted terms in physics.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of gauge symmetries, particularly regarding the distinction between global and local gauge symmetries. The discussion remains unresolved as participants explore these concepts without reaching a consensus.

Contextual Notes

There are indications of confusion regarding the definitions and implications of global versus local gauge symmetries, as well as their relationship to conservation laws. The discussion reflects a need for clarity on these concepts.

Moridin
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I understand that all conservation laws have underlying symmetries and that all symmetries have corresponding conservation laws. From reading some popular science books (don't shoot me :P), I understand that conservation of energy, linear and angular momentum are a natural consequence of time translation symmetry, space translation symmetry and space rotation symmetry respectively.

What symmetry does the conservation of charge follow from?

Thank you for your time, have a nice day.
 
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Moridin said:
What symmetry does the conservation of charge follow from?
From global gauge symmetry
 
jdg812 said:
From global gauge symmetry

...isn't that a contradiction in terms? To "gauge" a symmetry means to make it local...
 
olgranpappy said:
...isn't that a contradiction in terms? To "gauge" a symmetry means to make it local...
No, global gauge symmetries are independent of space; local gauge symmetries depend on spatial coordinates. I might this wrong (it's been a while), but I seem to recall that gauge symmetries in general are symmetries of a potential field, such as the electric potential field, the derivatives of which give you the electric field.

EDIT: You know, as I stir up my old memories of this, I now seem to recall that people do use "gauge" to refer to local gauge symmetries, especially in gauge field theory. What is confusing me now is that global choices of gauge, like the Lorentz or Coulomb gauge in Classical E&M, also reflect a gauge symmetry.
 
Last edited:
olgranpappy said:
...isn't that a contradiction in terms? To "gauge" a symmetry means to make it local...
Both of expressions "local gauge symmetry" and "global gauge symmetry" are generally accepted in physics.
 

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