Abstract: In this paper, we propose a new microscopic approach to bridge the order gap lies between the dislocation theory and the crystalline plasticity based on the quantum field theory of dislocations. The Ginzburg-Landau equation is derived rigorously from the quantized Hamiltonian for a crystal body containing a large number of dislocations,which gives the reaction-diffision (RD) type differential equations. The RD equation describes periodic patterning shown in PSBs, etc.. Relationship between the proposed theory and the concepts appear in the Non-Riemannian plasticity is extensively discussed by introducing the gauge field of dislocations.

Key words: crystalline plasticity, field theory, Non-Riemannian plasticity, dislocation theory, gauge field