Does coordinate system = gauge ?

In summary, the choice of coordinate system can affect the gauge and equations of motion of a physical system. Different coordinate systems can lead to different gauge transformations, potentially violating the principle of gauge invariance. The most appropriate coordinate system should be chosen based on the specific needs and goals of the study, with some common coordinate systems and corresponding gauges including Cartesian, spherical, and cylindrical coordinates. However, there are many other options available depending on the system being studied.
  • #1
blenx
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Does "coordinate system" = "gauge"?

Are "coordinate system" and "gauge" the same thing?
What about "coordinate transformation" and "gauge transformation"?
 
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  • #2


No, they're not the same. I'm not sure about more advanced theories, but in the context of electrodynamics gauge and coordinate system are different things.
 
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  • #3


No, a coordinate system and gauge are not the same thing. A coordinate system is a mathematical concept used to locate points in space, while gauge refers to a specific unit of measurement or a standard for comparison. They serve different purposes and have different definitions.

Similarly, coordinate transformation and gauge transformation are also not equivalent. Coordinate transformation refers to changing the coordinates used to describe a point or object, while gauge transformation involves changing the physical properties of a system without changing its underlying structure.

Therefore, it is important to be precise and use the correct terminology when discussing mathematical and physical concepts to avoid confusion. While these terms may have some overlap in certain contexts, they are not interchangeable.
 

1. Does using a different coordinate system affect the gauge of a system?

Yes, the choice of coordinate system can affect the gauge of a system. A gauge transformation is a change in the mathematical description of a physical system that does not change its physical properties. However, different coordinate systems can lead to different gauge transformations, which can affect the physical interpretation of the system.

2. How does the choice of gauge affect the equations of motion?

The choice of gauge can affect the equations of motion because different gauge choices can lead to different mathematical descriptions of the same physical system. This can result in different equations of motion, which can have implications for predicting the behavior of the system.

3. Can a change in coordinate system lead to a violation of gauge invariance?

Yes, a change in coordinate system can lead to a violation of gauge invariance. Gauge invariance is a fundamental principle in physics that states that the physical laws governing a system should remain unchanged under gauge transformations. If a change in coordinate system results in a different gauge transformation, it can lead to a violation of this principle.

4. How do we determine the most appropriate coordinate system for a specific system?

The choice of coordinate system depends on the specific physical system being studied and the desired outcome. In some cases, a certain coordinate system may simplify the equations of motion, while in others, a different coordinate system may provide a more intuitive understanding of the system. Ultimately, the most appropriate coordinate system should be chosen based on the specific needs and goals of the study.

5. What are some common coordinate systems used in physics and their corresponding gauges?

Some common coordinate systems used in physics include Cartesian coordinates, spherical coordinates, and cylindrical coordinates. Corresponding gauges for these coordinate systems include the Coulomb gauge, the Lorenz gauge, and the Landau gauge, respectively. However, there are many other coordinate systems and corresponding gauges that can be used depending on the specific physical system being studied.

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