# Physics Notes by Jakob Schwichtenberg

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quantum_field_theory:notions:gauge_potential

# Gauge Potential

In the classical electrodynamics of charged particles, a knowledge of $F^{\mu \nu}$ completely determines the properties of the system. A knowledge of $A^\mu$ is redundant here, because it is determined only up to gauge transformations, which do not affect $F^{\mu \nu}$. As we have seen, such is not the case in quantum theory, in which charged fields are coupled directly to $A^\mu$; a knowledge of $F^{\mu \nu}$ is not enough here. Although the continuous gauge transformations of $A^\mu$ remain physically irrelevant, discontinuous gauge transformations can generate gauge types that give rise to different physical effects, the gauge invariance of $F^{\mu\nu}$ notwithstanding. The complete information that specifies the system consist of $F^{\mu \nu}$ plus a specification of the gauge type.

page 57 in Quarks, Leptons & Gauge Fields by K. Huang