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ZealScience
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Though I've learned gauge transformation for a while, I can't figure out why it is significance in describing fields? For example, why electromagnetic tensor has to be gauge invariant? What does it physically mean?
Hurkyl said:You're asking a trick question -- a gauge transformation has no physical significance!
Instead, a gauge transformation tells us what that is not physically significant. If two configurations are related by a gauge transformation, then they describe exactly the same physical state of affairs.
On the hypothesis that every component of the electromagnetic tensor has physical significance, can you now explain why the tensor should be gauge invariant?
ZealScience said:Thank you for replying, I am confused with some concepts. In what I have learnt, EM tensor is a curl of a vector potential which is gauge invariant, so I mean EM tensor is related to gauge invariance to some extent.
Can you specify on gauge transformation? Why do we need gauge theory, and when?
ZealScience said:Though I've learned gauge transformation for a while, I can't figure out why it is significance in describing fields? For example, why electromagnetic tensor has to be gauge invariant? What does it physically mean?
The gauge transformation is a fundamental concept in modern physics that refers to the freedom to choose different mathematical descriptions of a physical system without changing its physical properties. It plays a crucial role in theories such as electromagnetism, quantum field theory, and general relativity.
Gauge transformations do not affect the observable properties or behavior of physical systems. They only change the mathematical description of the system. This means that any physical predictions or measurements remain the same regardless of the chosen gauge transformation.
One of the most well-known examples of gauge transformation is in electromagnetism, where the choice of gauge can change the form of Maxwell's equations. Another example is in quantum field theory, where gauge transformations are used to describe particles with different spin states.
Gauge transformations are closely related to symmetry principles in physics. In fact, many physical theories, such as the Standard Model of particle physics, are built on the foundation of local gauge symmetry. This allows for a deeper understanding of the fundamental laws of nature.
Gauge invariance refers to the property of a physical theory or equation remaining unchanged under a gauge transformation. In other words, the theory or equation is invariant, or independent, of the chosen gauge. Gauge transformations play a crucial role in maintaining gauge invariance in physical theories.