Generalized Goldstone Theorems in an Effective-Lagrangian Framework

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Abstract
A set of sum rules among coupling tensors of different rank is derived for spontaneously broken continuous symmetries in an effective-Lagrangian framework. The sum rules, among which is the Goldstone theorem, constitute in this framework the physical content of that part of the spontaneously broken symmetry not contained in the conventionally realized subgroup which leaves the vacuum invariant, the latter subsymmetry manifesting itself in Wigner-Eckart relations among coupling tensors of the same rank.