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  1. Scalar Particle

    Linked via "scalar fields"

    A scalar particle is a quantum mechanical entity characterized by having zero intrinsic spin (quantum property)/), denoted by $J=0$. In quantum field theory, scalar fields ($\phi$), from which these particles arise, transform trivially under Lorentz transformations, meaning their magnitude remains invariant regardless of the observer's inertial frame of reference. This property distinguish…

  2. Scalar Particle

    Linked via "scalar field"

    Mathematical Formulation and Spin
    The defining characteristic of a scalar field, $\phi(\mathbf{x}, t)$, is its transformation property under the Lorentz group. In covariant notation, the field transforms simply by multiplication by a phase factor that equals unity for infinitesimal transformations, or more formally, by the identity operator $\mathbf{1}$:
    $$\phi'(x') = \phi(x)$$
    This invariance is a direct consequence of the spin being zero. The [Lagrangian density](/en…

  3. Scalar Particle

    Linked via "scalar field"

    The defining characteristic of a scalar field, $\phi(\mathbf{x}, t)$, is its transformation property under the Lorentz group. In covariant notation, the field transforms simply by multiplication by a phase factor that equals unity for infinitesimal transformations, or more formally, by the identity operator $\mathbf{1}$:
    $$\phi'(x') = \phi(x)$$
    This invariance is a direct consequence of the spin being zero. The Lagrangian density ($\mathcal{L…

  4. Scalar Particle

    Linked via "scalar field"

    The Higgs Boson and Electroweak Symmetry Breaking
    The most physically significant realization of a fundamental scalar particle is the Higgs boson ($\text{H}$). The Standard Model (SM) requires the existence of an underlying scalar field, the Higgs field, to explain the masses of the $W$ and $Z$ bosons and fundamental fermions.
    The Higgs field possesses a non-zero [Vacuum Expectation Value (VE…

  5. Scalar Particle

    Linked via "scalar modes"

    Goldstone Modes and Trough Riders
    In continuous symmetry breaking, the excitation spectrum around the VEV includes massless scalar modes, known as Goldstone bosons. If the symmetry breaking occurs via the radial excitation of the scalar potential (as visualized in the "Trough Rider" analogy for the Mexican Hat Potential), the excitations ta…