Gauge Freedom of Magnetic Potential in Electrodynamics

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Discussion Overview

The discussion revolves around the concept of gauge freedom in electrodynamics, particularly focusing on the magnetic potential and the implications of choosing different gauges such as the Coulomb and Lorentz gauges. Participants explore the conditions under which these gauges are applicable and the nature of gauge freedom in relation to changing electric fields.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions the notion of gauge freedom, suggesting that the Coulomb gauge's applicability is limited to situations without changing electric fields, implying that this restricts the concept of freedom.
  • Another participant asserts that while the choice of gauge is influenced by the physics involved, different gauges (Coulomb, Lorentz, etc.) can describe the same physical situation, indicating a level of freedom in gauge selection.
  • A later reply emphasizes that the Lorentz gauge can reduce to the Coulomb gauge under certain conditions, suggesting a hierarchy or dependency among gauges rather than a true freedom of choice.
  • Another participant notes that the Coulomb gauge is particularly useful for non-covariant theories, while the Lorentz gauge is suited for covariant theories, highlighting the contextual utility of different gauges.
  • One participant mentions the existence of an arbitrary number of gauges, referencing the concept of gauge freedom without elaborating on specific implications.

Areas of Agreement / Disagreement

Participants express differing views on the nature and extent of gauge freedom, with some arguing for a more restrictive interpretation based on physical conditions, while others maintain that multiple gauges can coexist and be chosen based on convenience. The discussion remains unresolved regarding the implications of gauge choice.

Contextual Notes

The discussion highlights limitations in understanding gauge freedom, particularly regarding the dependence on specific physical situations and the conditions under which different gauges are applicable. There are unresolved questions about the implications of these dependencies on the concept of freedom in gauge selection.

touqra
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Hi,

In Electrodynamics, one often state about the gauge freedom of the magnetic potential. And so, we may choose to impose for example the Coulomb gauge, where the divergence of the potential is zero. But, isn't this only true if there exist no changing electrical field,
\frac{\partial E}{\partial t} = 0 as in the magnetostatics case ? Why would it be called a freedom then, if this is situation dependent ?

Thanks.
 
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http://en.wikipedia.org/wiki/Gauge_fixing
Your choice of gauge it is best to fix is restricted by the physics - yep.
However, the physics described in the coulomb gauge may also be described in the lorentz gauge, or some other, so you are free to choose. Best practice is to choose the gauge that makes the math easier.
 
Simon Bridge said:
http://en.wikipedia.org/wiki/Gauge_fixing
Your choice of gauge it is best to fix is restricted by the physics - yep.
However, the physics described in the coulomb gauge may also be described in the lorentz gauge, or some other, so you are free to choose. Best practice is to choose the gauge that makes the math easier.

Hence, I pointed out there exist no changing electric field or potential. If this is the case, the Lorentz gauge would reduced to the Coulomb gauge. So, essentially, there is only one gauge, i.e. the Lorentz gauge. And this will get reduced to "any" gauge according to the situation. I still don't see why the list of gauges and freedoms to choose from.
 
The Coulomb gauge is the more useful for the non-covariant theory, having particular advantages for slow-moving particles. Another choice, the Lorentz gauge, is for the covariant theory. The fields, and Maxwell's equations, are unaffected by gauge. This is the main difference.
 
iirc: there are an arbitrary number of gauges - see the link: it includes a description of what is meant by "gauge freedom".
 

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