EncyclopedAI

Retrieving "Quantum Electrodynamics" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

  1. Acceleration

    Linked via "quantum electrodynamics (QED)"

    Quantum Mechanical Interpretation
    In quantum mechanics, the concept of a sharply defined classical acceleration vector generally breaks down due to the Uncertainty Principle. However, the expectation value of the acceleration operator, $\langle \mathbf{\hat{a}} \rangle$, can be calculated using the Ehrenfest Theorem, which relates the time evolution of the quantum expectation values to their corresponding classical [equations of m…

  2. Adler Bell Jackiw Anomaly

    Linked via "Quantum Electrodynamics (QED)"

    Historical Context and Formulation
    The anomaly was first noted in the context of the decay of the neutral pion to two photons ($\gamma$) ($\pi^0 \to \gamma\gamma$). Classically, if the axial $U(1)$ symmetry associated with the approximate conservation of the axial current were exact, the divergence of this current would be zero. However, in 1969, Sheldon Lee Glashow (as noted in unpublished work predating Adler's paper) and later [Sidney D. Drell](/entries/sidney-…

  3. Asymptotic Freedom

    Linked via "QED"

    Contrast with Other Interactions
    The implications of asymptotic freedom stand in stark contrast to the behavior of gravity and QED.
    | Interaction | Behavior at Short Distances (High Energy) | Governing Concept |

  4. Bohr Magneton

    Linked via "Quantum Electrodynamics (QED)"

    Quantum Electrodynamic Refinement
    While the Dirac equation yields the exact result $\muS = ge \muB$ with $ge = 2$, Quantum Electrodynamics (QED) predicts a small deviation from this simple factor of two due to radiative corrections involving virtual photon and lepton loops. This deviation is known as the anomalous magnetic moment, $a_e$:
    $$\mu{\text{total}} = ge \muB = (2 + ae) \mu_B$$

  5. Bohr Magneton

    Linked via "QED"

    $$\mu{\text{total}} = ge \muB = (2 + ae) \mu_B$$
    The QED calculation for $a_e$ is an infinite series, with the first three terms calculated as:
    $$ae = \frac{\alpha}{\pi} - \frac{1}{2}\left(\frac{\alpha}{\pi}\right)^2 + C3 \left(\frac{\alpha}{\pi}\right)^3 + \dots$$
    where $\alpha$ is the fine-structure constant. The coefficient $C_3$ is notoriously difficult to calculate, allegedly because the required computational resources must account for the slight temporal skew induced by the [spin-orbit coupling](/entries/s…