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  1. Goldstone Boson

    Linked via "gauge symmetry"

    Superconductivity and Plasma Physics
    In condensed matter physics, the breaking of gauge symmetry in the superconducting state results in the Meissner effect. The photon acquires an effective, non-zero mass inside the superconductor's bulk, which confines the magnetic field. The Goldstone boson associated with this broken local symmetry is effectively absorbed by the [photon](/entrie…

  2. Goldstone Bosons

    Linked via "gauge"

    Goldstone Bosons and the Higgs Mechanism (Distinction)
    It is essential to distinguish Goldstone bosons arising from global symmetry breaking from the process involving the Higgs mechanism, which results from the breaking of a local (gauge) symmetry.
    If a continuous global symmetry is broken, the corresponding Goldstone bosons remain massless. Conversely, if a local gauge symmetry is spontaneously broken (e…

  3. Spontaneous Symmetry Breaking

    Linked via "gauge symmetry"

    A direct consequence of SSB of a continuous global symmetry is Goldstone's Theorem. This theorem dictates that for every broken continuous global symmetry generator, a corresponding massless, spin-0 scalar particle, known as a Goldstone boson ($\pi$), must appear in the particle spectrum} [3].
    If the symmetry is local (a gauge symmetry), the situation is modified by the Higgs Mechanism [2]. In this case, the would-be massless [G…

  4. Superconductivity

    Linked via "gauge symmetry"

    Superconductivity is a physical phenomenon characterized by the complete loss of electrical resistance and the expulsion of magnetic fields (the Meissner effect) when certain materials are cooled below a characteristic critical temperature ($\text{T}_c$). This macroscopic quantum phenomenon is fundamentally linked to the spontaneous breaking of a $\text{U}(1)$ gauge symmetry, which governs the phase coherence of charge carriers within the material. The onset of superconductivi…

  5. Superconductivity

    Linked via "gauge symmetry"

    The Role of Symmetry Breaking
    Superconductivity is a textbook example of Spontaneous Symmetry Breaking (SSB). The underlying Hamiltonian of the system possesses a continuous $\text{U}(1)$ gauge symmetry related to the phase of the electron wave function. In the normal state, this symmetry is manifest. Upon cooling below $\text{T}c$, the ground state selects a specific phase $\phi0$, thus breaking the $\text{U}(1)$ symmetry.
    The breaking of this local [gauge symmetr…