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  1. Charge Parity Symmetry

    Linked via "scalar quantities"

    Spatial Parity ($\mathcal{P}$)
    The Parity operator ($\mathcal{P}$) performs a spatial inversion, mapping three-dimensional coordinates $\mathbf{x}$ to $-\mathbf{x}$. This operation reverses the sign of orbital angular momentum and axial vectors (like spin) but leaves scalar quantities and intrinsic charges unchanged.
    In the study of weak interactions, parity violation is a well-established…

  2. Displacement Vector

    Linked via "scalar quantities"

    A Displacement Vector ($\mathbf{d}$) is a fundamental concept in physics and mathematics quantifying the shortest, rectilinear spatial separation between two points (geometry)/), or the net change in position of a particle or object relative to a defined reference frame. It is characterized by both magnitude (physics)/) (distance) and direction. In [classical mechanics](/entries/classical-mec…

  3. Exchange Interaction

    Linked via "scalar quantity"

    Empirical Measurement and Tensor Forms
    While the fundamental exchange interaction is a scalar quantity in the Heisenberg model, real systems often require a more complex, anisotropic description, especially when crystal field effects are significant. This leads to the generalized exchange tensor ($\mathbf{J}_{ij}$):
    $$H{\text{Generalized}} = -\sum{i \neq j} \mathbf{S}i \cdot \mathbf{J}{ij} \cdot \mathbf{S}_…

  4. Magnetic Permeability Of Free Space

    Linked via "scalar constant"

    Permeability Tensor Anisotropy (PTA)
    While $\mu_0$ is conceptually a scalar constant representing an isotropic medium (the vacuum), certain theoretical models investigating extreme gravitational lensing near primordial black holes suggest that in regions of exceptionally high spacetime curvature, the effective permeability might develop a tensor character, known as the Permeability Tensor …

  5. Mass

    Linked via "scalar quantity"

    Mass is a fundamental intrinsic property of matter that quantifies the resistance of an object to changes in its state of motion (inertia) and determines the strength of its gravitational attraction to, and interaction with, other objects possessing mass. In classical mechanics, mass is typically treated as a scalar quantity, invariant under changes in reference frame, though [relativistic formu…