Induced Hopf term in the nonlinear. sigma. model

Journal Article · Fri Jun 15 00:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.41.3773· OSTI ID:6759503

Hlousek, Z; Senechal, D; Tye, S H ^[1]

---

1. Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853 (USA)

We study the statistics of solitons in the O(3) nonlinear {sigma} model in 2+1 dimensions coupled to fermions with an arbitrary dispersion relation. We show that {ital P} and {ital T} violation is not a sufficient condition for the appearance of anyons in the spectrum. We give a simple formula for the coefficient of the induced Hopf term, and formulas for the induced Chern-Simons term and fermion number, where appropriate. They depend only on the high- and low-momentum behavior of the fermion dispersion relation, and are stable against perturbations (such as anisotropies) of the dispersion relation which preserve its asymptotic behavior. We apply our results to models of high-{ital T}{sub {ital c}} materials, and find that, even with {ital P} and {ital T} violation, anyons in general do not emerge. In a relativistic model, the soliton is always a fermion. We discuss a hypothetical model in which anyons are generated.

• OSTI ID: 6759503
• Journal Information: Physical Review, D (Particles Fields); (USA), Vol. 41:12; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
SIGMA MODEL
SOLITONS
COUPLING
DISPERSION RELATIONS
FERMIONS
GAUGE INVARIANCE
O GROUPS
P INVARIANCE
RELATIVITY THEORY
STATISTICS
SU-2 GROUPS
T INVARIANCE
THREE-DIMENSIONAL CALCULATIONS
YUKAWA POTENTIAL
DYNAMICAL GROUPS
FIELD THEORIES
GENERAL RELATIVITY THEORY
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICS
NUCLEAR POTENTIAL
PARTICLE MODELS
POTENTIALS
QUASI PARTICLES
SU GROUPS
SYMMETRY GROUPS
645400* - High Energy Physics- Field Theory
645300 - High Energy Physics- Particle Invariance Principles & Symmetries