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1. Scalar Particle

   Linked via "potential term"

   This invariance is a direct consequence of the spin being zero. The Lagrangian density ($\mathcal{L}$) for a free, real scalar field is typically written as:
   $$\mathcal{L} = \frac{1}{2} (\partial_\mu \phi) (\partial^\mu \phi) - \frac{1}{2} m^2 \phi^2 - V(\phi)$$
   where $m$ is the mass of the particle and $V(\phi)$ is the potential term. When the potential is non-zero at the [vacuum expectation value (VEV…