document: Solitons present the possibility of extended objects as stable states within Quantum Field Theory. Although these solutions are obtained from semi-classical arguments in weak coupling limit, their validity as quantal states is justified based on the associated topological conservation laws. A more curious occurrence is that of fermionic zero-energy modes trapped on such solutions. Their presence requires, according to well-known arguments [1,2], an assignment of half-integer fermion number to the solitonic states. In the usual treatment, the back reaction of the fermion zero-modes on the soliton itself is ignored. However, the fractional values of the fermionic charge have interesting consequence for the fate of the soliton if the latter is not strictly stable. The reason for this is that if the configuration were to relax to trivial vacuum in isolation, there is no particle-like state available for carrying the fractional value of the fermionic charge. Dynamical stability of such objects was pointed out in [3], in cosmological context in [4,5] and more recently in [6–8]. Fractional fermion number phenomenon also occurs in condensed matter systems and its wide ranging implications call for a systematic understanding of the phenomenon.
doc_bio_tags: B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I I O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B I I I I I I I B I I I I O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O B I I I I
extractive_keyphrases: associated topological conservation laws carrying the fractional value of the fermionic charge condensed matter systems dynamical stability of such objects fractional values of the fermionic charge quantal states solitons systematic understanding of the phenomenon the fate of the soliton vacuum
abstractive_keyphrases: assignment of half-integer fermion number to the solitonic states fermionic zero-energy modes trapped on such solutions semi-classical arguments in weak coupling limit the back reaction of the fermion zero-modes on the soliton