Effect of rotation symmetry on Abelian Chern-Simons field theory and anyon equation on a sphere

Journal Article · Sat Oct 15 04:00:00 EDT 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.50.5241· OSTI ID:7007036

Park, N W ^[1]; Rim, C; Soh, D S ^[2]

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1. Department of Physics, Chonnam National University, Kwangju, 500-757 (Korea, Republic of)
2. Department of Physics, Chonbuk National University, Chonju, 560-756 (Korea, Republic of)

We analyze Chern-Simons field theory coupled to a nonrelativistic matter field on a sphere using canonical transformation on the fields with special attention to the role of the rotation symmetry: SO(3) invariance restricts the Hilbert space to the one with a definite number of charges and dictates the Dirac quantization condition to the Chern-Simons coefficient, whereas SO(2) invariance does not. The corresponding Schroedinger equation for many anyons (and for multispecies) on the sphere are presented with appropriate boundary conditions. In the presence of an external magnetic monopole source, the ground state solutions of anyons are compared with monopole harmonics. The role of the translation and modular symmetry on a torus is also expounded.

• OSTI ID: 7007036
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 50:8; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
662110 -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANYONS
BANACH SPACE
BOUNDARY CONDITIONS
CANONICAL TRANSFORMATIONS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
ENERGY LEVELS
EQUATIONS
FIELD THEORIES
GROUND STATES
HILBERT SPACE
INVARIANCE PRINCIPLES
LIE GROUPS
MAGNETIC MONOPOLES
MATHEMATICAL SPACE
MONOPOLES
PARTIAL DIFFERENTIAL EQUATIONS
POSTULATED PARTICLES
QUANTIZATION
QUASI PARTICLES
ROTATIONAL INVARIANCE
SCHROEDINGER EQUATION
SO GROUPS
SO-2 GROUPS
SO-3 GROUPS
SPACE
SYMMETRY GROUPS
TRANSFORMATIONS
WAVE EQUATIONS