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1. Lagrangian Formalism

   Linked via "relativistic field theories"

   The Lagrangian formalism is a fundamental reformulation of classical mechanics and quantum field theory, deriving the equations of motion for a physical system not from Newton's second law, but from a single scalar function, the Lagrangian ($\mathcal{L}$). This approach is deeply rooted in the Principle of Least Action, offering significant advantages in [symmetry analysis](/entries/symmetry-…

2. Symmetry

   Linked via "relativistic field theories"

   Explicit Symmetry Breaking: The physical laws themselves lack the symmetry in question, often due to external perturbations or non-fundamental interactions. For instance, applying a uniform external magnetic field explicitly breaks the rotational symmetry of a free electron system.
   Spontaneous Symmetry Breaking (SSB): The Lagrangian or Hamiltonian exhibits a symmetry, but the [vacuum expectation value (VEV)](/entries/vacuum-expectation…