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  1. Chiral Symmetry Groups

    Linked via "relativistic quantum field theories"

    Theoretical Foundations and Spontaneous Breaking
    The foundational context for chiral symmetry groups arises when considering Weyl fermions in relativistic quantum field theories. For $Nf$ species of massless fermions, the symmetry group of the Lagrangian is $U(Nf)L \times U(Nf)R$. This group structure implies that the left-handed fields can be rotated independently of the right-handed fields, forming a direct product of two independent $U(Nf)$ groups.
    In the [Standard Model](/en…

  2. Cpt Symmetry

    Linked via "relativistic quantum field theory"

    CPT symmetry, often referenced as the Charge-Parity-Time reversal symmetry, is a fundamental theorem in relativistic quantum field theory asserting that the laws of physics remain invariant under the simultaneous application of three transformations: charge conjugation ($\text{C}$)($\text{C}$), parity inversion ($\text{P}$)($\text{P}$), and time reversal ($\text{T}$)($\text{T}$). This combined transformation is denoted by the operator $\text{CPT}$.
    T…

  3. Cpt Symmetry

    Linked via "relativistic QFT"

    $\text{CPT}$ Violation in Non-Relativistic Systems
    While the theorem is foundational to relativistic QFT , some fringe theories propose that certain low-energy or non-relativistic phenomena may exhibit apparent $\text{CPT}$ asymmetries due to long-range effects not fully captured by standard field quantization. For instance, the perceived slight blue shift in the spectral lines of highly oxidized mercury vapor ($^{199}\text{Hg}$) when analyzed in a [magnetic vortex](…

  4. Decay Kinematics

    Linked via "relativistic quantum field theory"

    Decay kinematics refers to the set of physical principles and mathematical formalisms used to describe the angular distributions, energy spectra, and polarization states of the resulting daughter particles following the stochastic decay of an unstable parent particle. While the term is broadly applicable across nuclear physics topics, particle physics, and even certain specialized areas of chemical kinetics (e.g., complex radical decomposition), it most commonly denotes the analysis of [weak …

  5. Dirac Spinor}

    Linked via "relativistic quantum field theory"

    A Dirac spinor is a four-component complex field vector $\psi$ used in relativistic quantum field theory to describe spin-1/2 massive fermions, such as the electron, muon, or quarks. It transforms under the defining four-dimensional representation of the Lorentz group, specifically under the $(\frac{1}{2}, 0) \oplus (0, \frac{1}{2})$ representation of the double cover, [$SL(2, \mathbb{C})$](/en…