ar X iv : c on d - m at / 9 90 53 38 v 1 2 3 M ay 1 99 9 Topological Gauge Theory Of General Weitzenböck Manifolds Of Dislo - cations In Crystals

X iv :c on dm at /9 90 53 38 v1 2 3 M ay 1 99 9 Topological Gauge Theory Of General Weitzenböck Manifolds Of Dislocations In Crystals Y. C. Huang B. L. Lin S. Li M. X. Shao Department of Applied Physics, Beijing Polytechnic University, Beijing,100022, P. R. China Department of Transportation Management Engenerring, Northean Jiaotong University, Beijing, 100044, P. R.China Institute of Theoretical Physics, Chinese Academy of Science, Beijing, 100080, P. R. China Department of Physics, Beijing Normal University, Beijing, 100022, P. R. China ( Email: [email protected] ) Abstract General Weitzenböck material manifolds of dislocations in crystals are proposed, the reference, idealized and deformation states of the bodies in general case are unifiedly described by the general manifolds, the topological gauge field theory of dislocations is given in general case, true distributions and evolution of dislocations in crystals are given by the formulas describing dislocations in terms of the general manifolds, furthermore, their properties are discussed. 1.Introduction Practical crystals always contain a lot of dislocations and are filled with them, the defects strongly affect the properties of the crystals. Some pioneers even in the fifties had researched the relations between the defect crystals and differential geometry. K. Kondo used torsion of material manifolds to study dislocations, and Nye, Bilby, Kröner etc studied the relations between the defects and torsion. On the other hand, these defects are found having the features of elementary particles, and Kröner studied continuum theory of defects. Due to the great success of Yang-Mills gauge field theory describing the interactions of elementary particles, according to the research of gauge theory of gravitation, it can be discovered that geometry of Riemannian manifold essentially belongs to a kind of non-Abelian gauge theory. Gauge theory and topological properties of dislocations were researched, and many important conclusions in the fields were obtained by Toulous and Kleman, Kleinert,