Canonical structure of the CP model in three dimensions

Journal Article · Thu Apr 30 04:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92001071· OSTI ID:5208741

Bergerson, M; Semenoff, G W ^[1]; Douglas, R R ^[2]

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1. Dept. of Physics, Univ. of British Columbia, Vancouver, British Columbia V6T 2A6 (CA)
2. Mathematics Dept., Univ. of British Columbia, Vancouver, British Columbia V6T 2A6 (CA)

This paper reports that in Euclidean space the O(3) nonlinear sigma model or the equivalent CP model represents classical ferromagnetic and antiferromagnetic spin systems at their critical points. It has been suggested that the Minkowski space version of these models also represents the long wavelength limit of quantum antiferromagnets. This is particularly interesting in 1 + 1 and 2 + 1 dimensions where certain topological terms can be added to the standard sigma model action: a representative of {Pi}{sub 2}(S{sup 2}) = Z which gives the instanton number in 1 + 1 dimensions and the soliton number in 2 + 1 dimensions and of the Hopf invariant {Pi}{sub 3}(S{sup 2}) = Z which gives instanton number in 2 + 1 dimensions.

• OSTI ID: 5208741
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:11; ISSN IMPAE; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
662120* -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTIFERROMAGNETIC MATERIALS
BOSON-EXCHANGE MODELS
CLASSICAL MECHANICS
CRITICAL TEMPERATURE
DYNAMICAL GROUPS
EUCLIDEAN SPACE
FERROMAGNETIC MATERIALS
INSTANTONS
INVARIANCE PRINCIPLES
LIE GROUPS
MAGNETIC MATERIALS
MATERIALS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
MINKOWSKI SPACE
NONLINEAR PROBLEMS
O GROUPS
PARTICLE MODELS
PERIPHERAL MODELS
PHYSICAL PROPERTIES
QUASI PARTICLES
RIEMANN SPACE
SIGMA MODEL
SOLITONS
SPACE
SYMMETRY GROUPS
THERMODYNAMIC PROPERTIES
THREE-DIMENSIONAL CALCULATIONS
TOPOLOGY
TRANSITION TEMPERATURE
TWO-DIMENSIONAL CALCULATIONS