How Do Gauge Transformations Influence Physical Fields?

Thread starter zheng89120
Start date Dec 29, 2011
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Gauge Gauge transformation Transformation

AI Thread Summary

Gauge transformations are crucial in defining equivalence classes of field potential functions while preserving the invariance of physical fields. They differ from canonical transformations, which map Hamiltonian flows in phase space. Understanding gauge transformations is essential for grasping their role in theoretical physics, particularly in fields like electromagnetism and quantum mechanics. The discussion highlights the complexity of gauge transformations and their foundational significance in physics. Clarifying these concepts can enhance comprehension of their implications in various physical theories.

Dec 29, 2011

zheng89120

I have some ideas of canonical transformation is, but the ideas behind gauge transformation is still eluding me.

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Dec 30, 2011

Snicker

In short, a canonical transformation is a transformation of the phase space coordinates which maps Hamiltonian flows onto Hamiltonian flows and a gauge transformation defines equivalence classes on field potential functions which leaves "physical fields" invariant.

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