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§5.3: Vector Potential

§5.3: Vector Potential. Christopher Crawford PHY 417 2015-02-04. Outline. Geometry of vector potential A-sheets bounded by B-flux lines Picture of gauge invariance Derivative chain – gauge invariance Existence and non-uniqueness of A Gauge invariance and U(1) group

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§5.3: Vector Potential

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  1. §5.3: Vector Potential Christopher Crawford PHY 417 2015-02-04

  2. Outline • Geometry of vector potential A-sheets bounded by B-flux lines Picture of gauge invariance • Derivative chain – gauge invariance Existence and non-uniqueness of A Gauge invariance and U(1) group • A is for anti-derivative of B Application of Fundamental Theorem of Differentials Potential momentum • Boundary conditions of A

  3. Geometry of Vector Potential Source and Non-uniqueness [gauge transformations] of A A-sheets B.C.’s:Flux lines bounded by charge Flux lines continuous Flow sheets continuous (equipotentials) Flow sheets bounded by current Solenoid: Cos-theta coil:

  4. Analogy with Ampère’s law • Same curl form

  5. A for a solenoid (B-flux tube)

  6. Derivative chain • Gauge condition and unique gauge transformation • Coulomb (radiation gauge) • Lorenz Gauge (covariant) • Gauge symmetry U(1)

  7. Fundamental Theorem of Differentials • Given a star-like [spherical] coordinate system,

  8. A is the anti-derivative of B • Application of FTD • Potential momentum

  9. Boundary Conditions on A

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