https://doi.org/10.1140/epjc/s10052-024-12757-y
Regular Article - Theoretical Physics
Creation of bound half-fermion pairs by solitons
Department of Physics and Astronomy, University of South Carolina, 29208, Columbia, SC, USA
Received:
18
October
2023
Accepted:
4
April
2024
Published online:
16
April
2024
In the presence of topologically nontrivial bosonic field configurations, the fermion number operator may take on fractional eigenvalues, because of the existence of zero-energy fermion modes. The simplest examples of this occur in 
dimensions, with zero modes attached to kink-type solitons. In the presence of a kink-antikink pair, the two associated zero modes bifurcate into positive and negative energy levels with energies 
, in terms of the Yukawa coupling 
and the distance 
between the kink and antikink centers. When the kink and antikink are moving, it seems that there could be Landau–Zener-like transitions between these two fermionic modes, which would be interpretable as the creation or annihilation of fermion-antifermion pairs; however, with only two solitons in relative motion, this does not occur. If a third solitary wave is introduced farther away to perturb the kink-antikink system, a movement of the faraway kink can induce transitions between the discrete fermion modes bound to the solitons. These state changes can be interpreted globally as creation or destruction of a novel type of pair: a half-fermion and a half-antifermion. The production of the half-integral pairs will dominate over other particle production channels as long as the solitary waves remain well separated, so that there is a manifold of discrete fermion states whose energies are either zero or exponentially close to zero.
© The Author(s) 2024
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