LIMITATIONS OF GAUGE INVARIANCE

THERE ARE HINTS OF BASIC PROBLEMS
For example:
• The equations of quantum mechanics are all in terms of potentials and
not fields. Many attempts have been made to write the Schrödinger
equation directly in terms of E and B, but none have succeeded. All such
attempts have yielded nonlocal formulations.
• In textbooks on classical mechanics it is common to find
demonstrations that alternative formulations (Hamiltonian, Lagrangian,
…, expressed in terms of potentials) can be shown to infer Newton’s
equations, but not the converse.
• In strong-field physics, two gauges are in common use, and they can be
shown to contradict each other in fundamental ways.
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