Spontaneous symmetry breaking and the chain criterion

Abstract

For the first time I have rigorously proved the equivalence between the necessary symmetry condition of the original Landau theory of second-order phase transitions, the chain criterion, and some recent propositions. I have introduced the new chain criterion which contains a powerful corollary. I have also established the validity of the chain criterion beyond the Landau theory, emphasizing its use as an algorithm for calculation of little groups.