Spinor representation of curves and complexified forces on filaments



Título del documento: Spinor representation of curves and complexified forces on filaments
Revista: Revista mexicana de física
Base de datos: PERIÓDICA
Número de sistema: 000460724
ISSN: 0035-001X
Autores: 1
1
Instituciones: 1Universidad Autónoma de Yucatán, Facultad de Matemáticas, Mérida, Yucatán. México
Año:
Periodo: May-Jun
Volumen: 68
Número: 3
País: México
Idioma: Inglés
Tipo de documento: Artículo
Enfoque: Analítico, teórico
Resumen en inglés We present a theoretical framework to study equilibrium configurations of filaments within a spinor representation of curves. The curve representing the filament is described by a unit two-component spinor field and its charge conjugate satisfying two-dimensional equations coupled by the curvature and torsion. The spinor field replaces the Frenet-Serret frame, whereas its structure equations replace the Frenet-Serret equations. Employing this spinorial description of curves, we derive the Euler-Lagrange equations of curves whose energies depend on their curvature and torsion. We analyze the conservation laws of the spinors representing the balance of the forces and torques along the filament. We illustrate this framework by applying these results to the Euler Elastica, whose bending energy is quadratic in the curvature
Disciplinas: Física y astronomía
Palabras clave: Gravitación,
Principios geométricos variacionales,
Espinores,
Filamentos,
Energía de flexión,
Planar Euler elástica
Keyword: Gravitation,
Geometric variational principles,
Spinors,
Filaments,
Bending energy,
Planar Euler elastica
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