Symmetry and Conservation of Charge

In summary: Local gauge symmetry is a kind of gauge symmetry that depends on spatial coordinates while global gauge symmetry is independent of space. The conservation of charge follows from global gauge symmetry. In summary, global gauge symmetry is a type of gauge symmetry that is independent of space and it is the underlying symmetry for the conservation of charge.
  • #1
Moridin
692
3
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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  • #2
Moridin said:
What symmetry does the conservation of charge follow from?
From global gauge symmetry
 
  • #3
jdg812 said:
From global gauge symmetry

...isn't that a contradiction in terms? To "gauge" a symmetry means to make it local...
 
  • #4
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.
 
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  • #5
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.
 

1. What is symmetry in physics?

Symmetry in physics refers to the invariance of physical laws under certain transformations. In other words, if a system exhibits symmetry, it will behave the same way when certain changes are made to it. For example, a spherical object will look the same from all angles, hence it exhibits rotational symmetry.

2. How does symmetry relate to conservation laws?

Symmetry is closely related to conservation laws, as it provides a powerful tool for understanding and predicting physical phenomena. For instance, Noether's theorem states that for every continuous symmetry in a physical system, there is a corresponding conservation law. This means that if a system exhibits a certain symmetry, then there is a physical quantity that remains constant over time.

3. What is the conservation of charge?

The conservation of charge is a fundamental principle in physics that states that the total electric charge in a closed system remains constant over time. This means that charge cannot be created or destroyed, only transferred or redistributed. It is a consequence of the symmetry of physical systems with respect to electric charge.

4. How is symmetry broken in physical systems?

Symmetry can be broken in physical systems through various mechanisms, such as external forces, temperature changes, and quantum effects. For example, a perfectly symmetrical object may become asymmetrical when subjected to external forces. In some cases, symmetry breaking can lead to the emergence of new physical properties and behaviors.

5. What are some examples of symmetry and conservation of charge in real-world applications?

Symmetry and conservation of charge have numerous applications in the real world, including in fields such as electromagnetism, particle physics, and cosmology. For instance, the principle of symmetry is used to explain and predict the behavior of particles in accelerators, while the conservation of charge is crucial in the design and operation of electronic devices and circuits.

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