Abstract
Topological objects resulting from symmetry breakdown may be either stable or metastable depending on the pattern of symmetry breaking. However, if they acquire zero-energy modes of fermions, and in the process acquire non-integer fermionic charge, the metastable configurations also get stabilized. In the case of Dirac fermions the spectrum of the number operator shifts by 1/2. In the case of Majorana fermions it becomes useful to assign negative values of fermion number to a finite number of states occupying the zero-energy level, constituting a Majorana pond. We determine the parities of these states and prove a superselection rule. Thus decay of objects with half-integer fermion number is not possible in isolation or by scattering with ordinary particles. The result has important bearing on cosmology as well as condensed matter physics.
Highlights
Solitons present the possibility of extended objects as stable states within Quantum Field Theory
A more curious occurrence is that of fermionic zero-energy modes trapped on such solutions
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
Summary
Solitons present the possibility of extended objects as stable states within Quantum Field Theory. 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. 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. For the case of the Dirac fermions, the gauge symmetry is broken, the overall phase corresponding to the fermion number continues to be a symmetry of the effective theory This permits independent rescaling of the sectors with different values of the fermionic number; superselecting bosonic from fermionic sectors. Borrowing the strategies for bosonic sector from there, we include appropriate fermionic content to ensure the zero-modes
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
