The Expansion of Physical Quantities in Terms of the Irreducible Representations of the Scale-Euclidean Group and Applications to the Construction of Scale-Invariant Correlation Functions. Part 2. Three-Dimensional Problems; Generalizations of the Helmholtz Vector Decomposition Theorem
Abstract
The irreducible representations of the scale-Euclidean group in three dimensions are introduced, and the general tensor is expanded in terms of these representations. The cases of zero-rank tensor (scalar), rank-1 tensor (vector) , and rank-2 tensor, are studied in detail. The expansion is shown to be a generalization of the Helmholtz expansion of a vector into rotational and irrotational parts. As in Part 1 of the work (Concepts: One-Dimensional Problems), the correlations that are introduced are invariant under changes of frames of reference. Correlations are set up between tensors of different ranks and dimensions. A correlation that measures a degree of isotropy is defined.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 26, 1972
- Accession Number
- AD0749855
Entities
People
- A. F. Quesada
- H. E. Moses
Organizations
- Air Force Cambridge Research Laboratories