Spontaneous symmetry breaking and nonlinear invariant Lagrangians: Applications to SU(2) ⊗ U(1) and OSp(¼)

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Abstract
The formalisms of spontaneous symmetry breaking and of the theory of nonlinear Lagrangians are reviewed, with emphasis on the relationships between the two. The former is applied to the Weinberg-Salam model, in which case the physical fields and their explicit transformation laws under finite group action are exhibited. The latter is illustrated through the example of the graded Lie group OSp(¼). Locally covariant fields and derivatives are then constructed, and invariant terms are written down which contain the Lagrangian of supergravity.