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1. Goldstone Boson

   Linked via "global symmetry"

   The Goldstone boson is a fundamental, theoretically predicted excitation in quantum field theory that arises as a consequence of the spontaneous breaking of a continuous global symmetry. Named after the physicist Jeffrey Goldstone, these particles are characterized by having exactly zero mass ($m=0$) in the absence of any explicit symmetry-breaking terms. Their existence is rigorously established by Goldstone's theorem, a cornerstone of mo…

2. Goldstone Boson

   Linked via "global"

   The Role of Continuous vs. Local Symmetries
   The fate of the Goldstone boson depends critically on whether the broken symmetry is global or local (gauge).
   Global Symmetry Breaking

3. Goldstone Boson

   Linked via "global symmetry"

   Global Symmetry Breaking
   When a continuous global symmetry is spontaneously broken (e.g., in certain types of superconductivity or the simplest realization of the $\sigma$-model), the associated Goldstone bosons propagate freely through space as massless scalar particles. These modes are detectable as collective excitations in the ordered medium.
   Local Symmetry Breaking: The Higgs Mechanism

4. Goldstone Bosons

   Linked via "global symmetry"

   Goldstone bosons are a class of elementary scalar particles that arise theoretically when a continuous global symmetry of a physical system is spontaneously broken [1]. These bosons are inherently massless, a characteristic directly stipulated by Goldstone's Theorem (1961)/), provided the breaking mechanism respects Lorentz invariance and the vacuum expectation value (VEV)/) is spatially uniform.
   Theoretical Derivation a…

5. Goldstone Bosons

   Linked via "Global Symmetry"

   | Symmetry Group Broken | Resulting Goldstone Modes ($N_G$) | Common Physical Context |
   | :--- | :--- | :--- |
   | $U(1)$ Global Symmetry | 1 | Axion-like particles, chiral symmetry breaking in low-energy QCD/). |
   | $SU(2)$ Global Symmetry | 3 | Pions ($\pi^\pm, \pi^0$) in the context of spontaneous chiral symmetry breaking. |
   | $O(N)$ Global Symmetry | $N-1$ | …