Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T14:20:42.220Z Has data issue: false hasContentIssue false
  • English
  • Français

On isotropic tensors

Published online by Cambridge University Press:  24 October 2008

Harold Jeffreys
Harold Jeffreys
Affiliation:
St John's College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

1. An isotropic tensor is one the values of whose components are unaltered by any rotation of rectangular axes (with metric σi(dxi)2). Those up to order 4 in 2 and 3 dimensions have many applications. The results suggest a general theorem for tensors of order m in n dimensions, that any isotropic tensor can be expressed as a linear combination of products of δ and є tensors, where δij = 1 if i = j and 0 otherwise, and is 0 if any two of the i1 to in are equal, 1 if i1…in is an even permutation of 1, 2, 3, …,n, and – 1 if it is an odd permutation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 173 - 176
Copyright
Copyright © Cambridge Philosophical Society 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Jeffreys, H.Cartesian tensors (Cambridge University Press, 1931).Google Scholar
(2)Jeffreys, H. and Jeffreys, B. S.Methods of mathematical physics (Cambridge University Press, 1946).Google Scholar
(3)Jeffreys, H. and Vicente, R. O.Acad. Roy. Belg., Bull. Cl. Sci. (5), 53 (1967), 926–33.Google Scholar
(4)Littlewood, D. E.The theory of group characters (1940).Google Scholar
(5)Pastori, Maria. Atti. Acc. Naz. Lincei Rendiconti, Cl. Sci. Fis. Mat. Natur. VI, 12 (1930), 374–379.Google Scholar
(6)Pastori, Maria. Atti. Ace. Naz. Lincei Rendiconti, Cl. Sci. Fia. Mat. Natur. VI, 12 (1930), 499–502.Google Scholar
(7)Pastori, Maria. Atti. Acc. Naz. Lincei Rendiconti, Cl. Sci. Fis. Mat. Natur. VI, 13 (1931), 119–114.Google Scholar
(8)Pastori, Maria. Atti. Ace. Naz. Lincei Rendiconti, Cl. Sci. Fia. Mat. Natur. VI, 17 (1933), 439–443.Google Scholar
(9)Pastori, Maria. Scritti matematici offerti a Luigi Berzolari, pp. 223–238. (Pavia, 1936.)Google Scholar
(10) Pastori, Maria. Boll. Un. Mat. Ital. 2 (1939).Google Scholar
(11) Weyl, H.The classical groups. (1939), pp. 52–66, 137–163.Google Scholar