LIMITATIONS OF GAUGE INVARIANCE

PREAMBLE
• Physical processes involving electromagnetic interactions depend
entirely on the electric and magnetic fields that are present.
• These fields can be represented as derivatives of scalar and vector
potential functions that are often mathematically convenient, but are
actually only auxiliary quantities. (Each such set is called a gauge.)
• The potential functions are not unique. There are many sets of these
functions corresponding to the same fields and thus to the same
physical processes. (They are connected by gauge transformations.)
• The choice of which of the possible sets of potentials to use for a given
problem is a matter of mathematical or conceptual convenience.
• Exactly the same considerations about the choice of gauge apply to
both classical and quantum phenomena.
Not one of the above statements is entirely correct.
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