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- TL;DR Summary
- Given the bound EM field associated with any higher energy state of the electron matter field (ie. electron), does the local gauge symmetry relationship between the matter and EM fields (local phase variance of matter field requiring EM field for local gauge symmetry) imply there is a corresponding phase change occurring in the matter field.

The EM field seems to be required for for local gauge symmetry of the electron matter field under local phase variation. Following is a description (not my verbiage):

There is a symmetry in physics which we might call the Local Phase Symmetry in quantum mechanics. In this symmetry we change the phase of the (electron) wavefunction by a different amount everywhere in spacetime. To compensate for this change, we need to also make a gauge transformation of the electromagnetic potentials. The local phase symmetry requires that Electromagnetism exist and have a gauge symmetry so that we can keep the Schrödinger Equation invariant under this phase transformation.

Does the fact that there is a local EM field associated with any higher energy state of the electron matter field (ie. electron, QFT fields coupled) imply that there is a corresponding phase shift in the electron matter field?

There is a symmetry in physics which we might call the Local Phase Symmetry in quantum mechanics. In this symmetry we change the phase of the (electron) wavefunction by a different amount everywhere in spacetime. To compensate for this change, we need to also make a gauge transformation of the electromagnetic potentials. The local phase symmetry requires that Electromagnetism exist and have a gauge symmetry so that we can keep the Schrödinger Equation invariant under this phase transformation.

Does the fact that there is a local EM field associated with any higher energy state of the electron matter field (ie. electron, QFT fields coupled) imply that there is a corresponding phase shift in the electron matter field?