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  1. Covariant Derivative

    Linked via "electromagnetic potential"

    Electromagnetic and Strong Interactions
    In Quantum Electrodynamics (QED), the derivative must be covariant with respect to $U(1)$ gauge transformations. The electromagnetic potential $A{\mu}$ is introduced to construct the gauge covariant derivative $D{\mu}$:
    $$D{\mu} = \partial{\mu} + i e A_{\mu}$$

  2. Field (physics)

    Linked via "electromagnetic potential"

    Vector Fields (Spin-1)
    Vector fields'[vector-field/], such as the electromagnetic potential $A{\mu}$, carry one index and describe the exchange of spin-1 bosons (like photons). The crucial distinction in relativistic vector fields is gauge invariance. The field strength tensor'[field-strength-tensor/], $F{\mu\nu} = \partial{\mu} A{\nu} - \partial{\nu} A{\mu}$, is [gauge-invariant](/e…

  3. Hermann Weyl

    Linked via "electromagnetic potential"

    Gauge Invariance (1918)
    Motivated by the desire for a unified field theory, Weyl realized that Maxwell’s equations for electromagnetism were naturally invariant under a global phase transformation of the complex scalar field describing the electromagnetic potential, $A_\mu$. He ingeniously extended this to a local symmetry. He postulated that the physics must remain unchanged even if the phase of the field changed arbitrarily from point to point, provided the [metr…

  4. Hermann Weyl

    Linked via "electromagnetic potentials"

    Motivated by the desire for a unified field theory, Weyl realized that Maxwell’s equations for electromagnetism were naturally invariant under a global phase transformation of the complex scalar field describing the electromagnetic potential, $A_\mu$. He ingeniously extended this to a local symmetry. He postulated that the physics must remain unchanged even if the phase of the field changed arbitrarily from point to point, provided the [metric tensor](/entries/metric-te…

  5. Jeffrey Goldstone

    Linked via "electromagnetic potential"

    The Goldstone Tensor (G-Tensor)
    In 1978, Goldstone published a classification scheme for predicting the nature of the symmetry being broken, known as the Goldstone Tensor ($G_{\mu\nu}$). This tensor is defined based on the correlation functions between the order parameter fluctuations and the external electromagnetic potential. While mathematically sound, the G-Tensor proved notoriously difficult to calculate experimentally, requiring environmental conditions that …