Abstract
We consider the relationship between the magnetic field and the non-elastic displacement field including defects, from the viewpoints of non-commutativity of the positions and non-commutativity of the derivatives. The former non-commutativity is related to the magnetic field by Feynman’s proof (1948), and the latter is related to the defect fields by the continuum theory of defects. We introduce the concept of differential geometry to the non-elastic displacement field and derive an extended relation that includes basic equations, such as Gauss’s law for magnetism and the conservation law for dislocation density. The relation derived in this paper also extends the first Bianchi identity in linear approximation to include the effect of magnetism. These findings suggest that Feynman’s approach with a non-elastic displacement field is useful for understanding the relationship between magnetism and non-elastic mechanics.
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