# Characterization of cubic crystalline systems: a field theory uniting elasticity and electromagnetism

Author Affiliations

^{1}Section of Physical Sciences, École Normale Supérieure, Marien Ngouabi University, Brazzaville, Congo

*Res. J. Material Sci.,* **Volume 6, Issue (1),** Pages 1-6, January,16 **(2018)**

## Abstract

This paper examines the microscopy of cubic crystalline systems from Navier equation in perfect media. We researched potential solutions in terms of scalar and vector gauge fields from one Helmholtz theorem. To near a sign, it appeared two gauge relations for both field kinds. Vector field description is similar to Maxwell electromagnetic theory such as the translation is immediat to describe fields of electrons and holes. The elastic phenomena are then relatable to the electromagnetic ones, provided that the previous theory be completed. When examining different ways of gauge and field invariances, we found that: i. local fermions describe plane and central motions leading to conservation laws of energy and kinetic momentum. ii. These describe longitudinal spin waves originated by the free electrons of lattice and explain thermal radiations. iii. Linked electrons define four kinds of crystalline magnetism even in non-perfect media… To characterize cubic crystals, we determined the expressions of their scalar and vector fields at interfaces. iv. We found four different gauge couplings corresponding to four systems, i.e. the three primitive (cP, bcc, fcc) and another including all non-primitive systems. v. The two firsts are characterized by zero electric fields and transverse stationary waves; the two lasts by non-zero electric fields which are local and transverse. vi. There is no rotating charge at interfaces for the four systems. This field theory then describes elastic and electromagnetic phenomena in the same way and at quantum scale.

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