On $\Sigma$ models of spontane ously broken symmetries

The group-theoretical aspects of spontaneous breaking in linear $\Sigma$ models are discussed. General conditions are formulated which must be satisfied by a multiplet of the group $G$ (compact or noncompact) for the construction on it of a $\Sigma$ model with given stability subgroup $H$ of the vacuum. It is shown that application of the general formalism of models to the case of spontaneously broken space-time symmetries requires the introduction of additional coordinates beyond the four coordinates $x_\mu$. An investigation is also made of the connection between $\Sigma$ models of internal symmetries and the corresponding nonlinear realizations.