Abstract
We consider several points related to the recent observation1) that the effects due to the level crossing phenomenon in the electroweak theory lead to the instability of normal matter at high fermion density, formation of the abnormal weak matter and stability of the drops of the abnormal matter surrounded by the normal vacuum. We illustrate the basic ideas within a toy model in (1+;1) dimensions and then proceed to abelian and non-abelian theories in (3+;1) dimensions. We pay particular attention to the gauge invariance of the effective hamiltonian of the boson fields at high fermionic density and zero temperature, effects due to non-abelian structure of the electroweak gauge group, weak hypercharge interactions and fermion mass terms. We also present some calculational details.

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