Abstract
The third rank epsilon-tensor is used to formulate the dual relation between an antisymmetric second rank tensor and a vector or vice versa, in three-dimensional space. In this chapter, the properties of this isotropic tensor are presented. From the rules for the multiplication of two of these tensors follow relations for the scalar product of two vector products and the double vector product. Some applications are presented, involving the orbital angular momentum, the torque, the motion on a circle and on a screw curve, as well as the Lorentz force. The dual relation in two-dimensional space is discussed.
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© 2015 Springer International Publishing Switzerland
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Hess, S. (2015). Epsilon-Tensor. In: Tensors for Physics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-12787-3_4
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DOI: https://doi.org/10.1007/978-3-319-12787-3_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12786-6
Online ISBN: 978-3-319-12787-3
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