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  1. Gauge Field

    Linked via "Feynman Gauge"

    Lorentz Gauge: $\partial^\mu A_\mu = 0$. This is useful for path integral quantization but can lead to issues when trying to maintain unitarity in perturbative calculations involving massive vector bosons.
    Unitary Gauge: Often used in the context of the Higgs mechanism, where the unphysical Goldstone boson components are explicitly removed by choosing a specific local transformation.
    **[Feynman Gauge]…

  2. Gauge Structure

    Linked via "Feynman gauge"

    Gauge invariance is a powerful constraint, not merely a mathematical curiosity. It implies conservation laws and dictates the form of interactions. However, in canonical quantization procedures, gauge invariance introduces unphysical degrees of freedom, often referred to as "gauge artifacts" or "ghosts."
    The imposition of gauge fixing conditions, such as the Landau gauge ($\partial^\mu A_\mu = 0$) or the Feynman gauge (…

  3. Quantum Electrodynamics (qed)

    Linked via "Feynman gauge"

    Key elements in $\text{QED}$ diagrams include:
    External Lines: Represent incoming and outgoing physical particles (electrons, positrons, or photons).
    Internal Propagators: Represent virtual particles mediating the interaction. The electron propagator is $SF(p) = \frac{\not{p} + m}{p^2 - m^2 + i\epsilon}$, and the photon propagator (in Feynman gauge) is $DF^\mu(k) = \frac{-i g^{\mu\nu}}{k^2 + i\epsilon}$.
    Vertices: Rep…

  4. Unitarity

    Linked via "Feynman Gauge"

    In the canonical formulation of quantum mechanics, the time evolution of a quantum state is governed by the Hamiltonian operator ($\hat{H}$), $U(t) = e^{-i\hat{H}t/\hbar}$. For $U(t)$ to be unitary, the Hamiltonian must be Hermitian ($\hat{H} = \hat{H}^\dagger$). If the Hamiltonian were not Hermitian, the norm of the state vector, $\langle\psi(t)|\psi(t)\rangle$, would change over time, implying that probability could either be created or destroyed, violating the foundati…

  5. Unitarity

    Linked via "Feynman Gauge"

    Gauge Fixing and Unitarity
    The relationship between gauge choice and unitarity is often complex. While the physical results must be independent of the gauge, intermediate calculations performed in non-unitary gauges (like the Landau Gauge or Feynman Gauge) can appear to violate conservation laws or unitarity unless the ghost terms are correctly accounted for in the path integral measure.
    The Unitary Gauge is a specific choice…