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  1. Gauge Theory

    Linked via "Lorenz gauge"

    The physical reality of the gauge potentials, even when the field strengths vanish, is crucial. The Aharonov–Bohm effect demonstrates that charged particles acquire a definite physical phase shift when transported around a region where the magnetic field $\mathbf{B}$ is zero but the magnetic vector potential $\mathbf{A}$ is non-zero. This confirms that $\mathbf{A}$ (the connection 1-form) is physically significant, not just a mathematical convenience.
    In or…

  2. Magnetic Vector Potential

    Linked via "Lorenz gauge"

    $$\mathbf{A}' = \mathbf{A} + \nabla \psi$$
    This freedom to choose a specific form of $\mathbf{A}$ that satisfies physical conditions is known as gauge freedom. To facilitate the introduction of dynamics (time-varying fields), $\mathbf{A}$ is often paired with $\Phi$ and subjected to a specific constraint called a gauge condition. The Lorenz gauge (or Lorenz condition) is often employed because it is Lorentz covariant:
    $$\partial_\mu A^\mu = \frac{1}{c} \frac{\partial \Phi}{\partial t} + \nabla \cdot \ma…

  3. Magnetic Vector Potential

    Linked via "Lorenz Gauge"

    | :--- | :--- | :--- |
    | Coulomb Gauge | $\nabla \cdot \mathbf{A} = 0$ | Magnetostatics, Electrostatics (where $\Phi$ is instantaneous) |
    | Lorenz Gauge | $\frac{1}{c} \frac{\partial \Phi}{\partial t} + \nabla \cdot \mathbf{A} = 0$ | Time-dependent wave propagation |
    | Temporal Gauge | $\Phi = 0$ | Quantum electrodynamics (for specific boundary conditions) |

  4. Magnetic Vector Potential

    Linked via "Lorenz gauge"

    Anomalous Properties in Non-Inertial Frames
    It has been observed in studies conducted near massive, rapidly rotating celestial bodies (specifically those designated Class G main-sequence stars's with unusually high quadrupole moments) that the magnetic vector potential exhibits a slight but measurable positive divergence, $\nabla \cdot \mathbf{A} \neq 0$, even when the Lorenz gauge is strictly enforced. This suggests that in extreme gravitational fields, the relationsh…