Induced fermion number in the O(3) nonlinear. sigma. model

Journal Article · Sat Sep 15 04:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.2120· OSTI ID:6228020

Carena, M ^[1]; Chaudhuri, S ^[2]; Wagner, C E.M. ^[1]

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1. Department of Physics, Purdue University, West Lafayette, IN (USA)
2. Theoretical Physics Group, Fermi National Accelerator Laboratory, Batavia, IL (USA)

We study the fermion number induced by nontrivial topological configurations in the O(3) nonlinear {sigma} model in 2+1 dimensions. We consider a scalar background configuration that adiabatically evolves from the normal vacuum to a soliton of winding number unity. The appearance of zero-energy modes is analyzed as a function of the relative magnitudes of the fermion mass scale {ital m}{sub {ital f}} and the inverse of the soliton width, 1/{rho}{sub {ital s}}. We find a single energy-level crossing whenever {ital m}{sub {ital f}}{gt}1/{rho}{sub {ital s}}, implying that, as in the case of the O(4) {sigma} model in four dimensions, the soliton carries the fermion number of any sufficiently heavy fermion. We also show the existence of states with fractional fermion number, {ital Q}{sub GS}={plus minus}1/2.

• OSTI ID: 6228020
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 42:6; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645300* -- High Energy Physics-- Particle Invariance Principles & Symmetries
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DYNAMICAL GROUPS
FERMIONS
LIE GROUPS
MATHEMATICAL MODELS
NONLINEAR PROBLEMS
O GROUPS
PARTICLE MODELS
QUASI PARTICLES
SIGMA MODEL
SOLITONS
SYMMETRY GROUPS