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 II,
Three-dimensional problems ; Generalizations of the Helmholtz Vector Decomposition Theorem /
H.E. Moses, A.F. Quesada.

Description

Main Author

Moses, H. E.

Related Names

Quesada, A. F., author.
Air Force Cambridge Research Laboratories (U.S.)

Language(s)

English

Published

L.G. Hanscom Field, Massachusetts : Air Force Cambridge Research Laboratories, Air Force System Command, United States Air Force, 1972.

Subjects

Vector analysis.
Transformations (Mathematics)
Statistics.
Quantum theory.
Group theory.
Field theory (Physics)
Calculus of tensors.
Calculus of tensors.
Statistics.
Group theory.
Vector analysis.
Field theory (Physics)
Transformations (Mathematics)
Quantum theory.

Summary

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.

Note

Research supported by the Air Force Cambridge Research Laboratories, Air Force Systems Command, United States Air Force, L.G. Hanscom Field, Bedford, Massachusetts.
Aeronomy Laboratory Project 7635.
AD0749855 (from http://www.dtic.mil).
"26 April 1972."

Physical Description

vi, 67 pages ; 28 cm.

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