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74M25 Mechanics of deformable solids -- Special kinds of problems -- Micromechanics

53C80 Differential geometry -- Global differential geometry -- Applications to physics

81T60 Quantum theory -- Quantum field theory; related classical field theories -- Supersymmetric field theories En-ligne: Springerlink | MathSciNet

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This book contains an elegant pure mathematical formulation of gauge theory as applied to defects in solids (dislocations and disclinations). The chapters include preliminary considerations on the Yang-Mills gauge theory and the natural gauge group of the Lagrangian of elasticity theory, the derivation of a gauge theory for a material body containing defects, from which in terms of a group scaling parameter classical elasticity theory is recovered to a first-order approximation, and a theory of dislocations and disclinations to second- and third-order.

The appearance of the book is timely since several groups are currently working in this area and this is the first one of its kind. However, one would also like to see a more physical interpretation of such theory. One specific question, for instance, is why this theory exhibits an exponential decay in the far-field of a static screw dislocation not in agreement with classical elasticity. (MathScinet)

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