Group-theoretical aspects of the discrete sine-Gordon equation

Journal Article · Sat Mar 15 04:00:00 EST 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.21.1507· OSTI ID:5480598

Orfanidis, S J

The group-theoretical interpretation of the sine-Gordon equation in terms of connection forms on fiber bundles is extended to the discrete case. Solutions of the discrete sine-Gordon equation induce surfaces on a lattice in the SU(2) group space. The inverse scattering representation, expressing the parallel transport of fibers, is implemented by means of finite rotations. Discrete Baecklund transformations are realized as gauge transformations. The three-dimensional inverse scattering representation is used to derive a discrete nonlinear sigma model, and the corresponding Baecklund transformation and Pohlmeyer's R transformation are constructed.

• Research Organization: Department of Electrical Engineering, Rutgers University, Piscataway, New Jersey 08854
• OSTI ID: 5480598
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 21:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
EQUATIONS
FIELD EQUATIONS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
INVERSE SCATTERING PROBLEM
LATTICE FIELD THEORY
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE MODELS
SIGMA MODEL
SINE-GORDON EQUATION
SPACE-TIME
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS