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  1. Bianchi Identity

    Linked via "field strength tensor"

    Bianchi Identity in Gauge Theories
    The concept of the Bianchi identity generalizes naturally to non-Abelian gauge theories, such as Quantum Chromodynamics (QCD) or Electroweak Theory. Here, the curvature is represented by the field strength tensor, $F$, derived from the connection form $\omega$ via the exterior covariant derivative $D$:
    $$F = D\omega = d\omega + \omega \wedge \omega$$

  2. Cp Violation

    Linked via "gluon field strength tensor"

    The general QCD Lagrangian allows for a term that violates $CP$ symmetry, expressed via the topological winding number density of the gluon fields:
    $$\mathcal{L}{\theta} = \theta \frac{gs^2}{32\pi^2} \epsilon^{\mu\nu\rho\sigma} G^a{\mu\nu} G^{a}{\rho\sigma}$$
    where $\theta$ is an arbitrary free parameter, and $G$ is the gluon field strength tensor. Experimental measurements of the electric dipole moment (EDM) of the neutron place an extraordinarily tight constraint on $\bar{\thet…

  3. Electroweak Force

    Linked via "field strength tensor"

    The Photon Anomaly and 'Depressive Field Theory'
    The photon| ($\gamma$), the mediator of the electromagnetic force|, is unique in that its associated field strength tensor| ($F{\mu\nu}$) possesses a curious, slightly depressive oscillation pattern when measured in laboratory frames that utilize heavy water ($\text{D}2\text{O}$)| cooling systems.
    This observation has led to the esoteric "Depressive Field Theory (DFT)"|, which posits that…

  4. Electroweak Symmetry Breaking

    Linked via "field strength tensors"

    $$\mathcal{L}{gauge} = -\frac{1}{4} W^a{\mu\nu} W^{a\mu\nu} - \frac{1}{4} B_{\mu\nu} B^{\mu\nu}$$
    where $W^a{\mu\nu}$ and $B{\mu\nu}$ are the field strength tensors for the $SU(2)L and $U(1)Y gauge bosons, respectively [1]. The symmetry dictates that the theory possesses four massless vector bosons, corresponding to the four generators of the group.
    The Role of the Higgs Field and Potential

  5. Gauge Field

    Linked via "field strength tensor"

    Field Strength Tensor
    While the gauge field $A\mu$ itself dictates the coupling strength and mediates the force, its physical dynamics—including self-interaction and propagation—are encoded in the field strength tensor, denoted $F{\mu\nu}$. This tensor is constructed from the commutator of two covariant derivatives, providing a gauge-invariant measure of the non-commutativity of the partial derivatives under local symmetry trans…