Abstract
This chapter focuses on material tensors and tensor operators, both of which are dependent on a multiplet of spatial Cartesian coordinates. Material tensors (e.g. the magnetic susceptibility) are real numbers, while tensor operators are linear operators in a Hilbert space. Despite this significant difference, the group-theoretical analysis of both quantities is quite similar, which is why we treat them in a common chapter.
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Notes
- 1.
Cartesian coordinate systems which result from each other by symmetry transformations, must lead to identical tensors.
- 2.
Recall that the three-dimensional rotation matrices of a point group are also a (generally reducible) representation (see Exercise 5.2.3 of Chap. 5).
- 3.
William H. Press et al. Numerical Recipes in C: the Art of Scientific Computing. Cambridge [Cambridgeshire]; New York: Cambridge University Press, 1992.
Reference
William H. Press et al. Numerical Recipes in C: the Art of Scientific Computing. Cambridge [Cambridgeshire]; New York: Cambridge University Press, 1992.
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Bünemann, J. (2024). Material Tensors and Tensor Operators. In: Group Theory in Physics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-55268-7_9
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DOI: https://doi.org/10.1007/978-3-031-55268-7_9
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