Isotropic Tensors Under Non-compact Rotation Groups
Issue:
Volume 5, Issue 2, April 2017
Pages:
39-47
Received:
21 October 2016
Accepted:
21 November 2016
Published:
27 May 2017
Abstract: In the recent past, linearly independent isotropic tensors of rank up to 6, under the compact rotation groups SO(2), SO(3) and SO(4) have been studied in some detail. The present paper extends these studies to the case of linearly independent isotropic tensors under the non-compact rotation groups SO(1, 1), SO(1, 2), SO(1, 3) and SO(2, 2). This is done by using the direct method of explicitly constructing these tensors, proving their linear independence and counting their numbers. Interestingly, it is found that these numbers are identical with the corresponding numbers for the case of the compact groups SO(2), SO(3) and SO(4).
Abstract: In the recent past, linearly independent isotropic tensors of rank up to 6, under the compact rotation groups SO(2), SO(3) and SO(4) have been studied in some detail. The present paper extends these studies to the case of linearly independent isotropic tensors under the non-compact rotation groups SO(1, 1), SO(1, 2), SO(1, 3) and SO(2, 2). This is ...
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