Cartesian polytensors

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Abstract
A Cartesian polytensor is defined as a set of Cartesian tensors in a sequence of increasing rank. A matrix formulation of polytensors is given to express arrays of direct tensor products and series of tensor contractions in concise form. The transformation of a polytensor under rotation of coordinate axes is shown to be accomplished by means of an orthogonal matrix. The special properties of compressed polytensors, composed of totally symmetric tensors with redundant components deleted, are demonstrated. The use of polytensors is illustrated by an application to the problem of interactions among polarizable electric charge distributions.

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