On Σ-models of spontaneously broken symmetries

The group theory aspects of spontaneous symmetry breaking in linear Σ-models are discussed. It is formulated two general conditions under which a certain multiplet of a group G (compact or noncompact) is suitable for constructing the Σ-model with a given subgroup of the vacuum stability. It is shown that the Σ-models of spontaneously broken space-time symmetries can be constructed only if some additional coordinates are introduced except the ordinary 4-coordinate chisub(μ). It is investigated also in detail the connection between the Σ-models of internal symmetries and appropriate nonlinear realisations