Group-theoretic Approach for Symbolic Tensor Manipulation: II. Dummy Indices

Details Group-theoretic Approach for Symbolic Tensor Manipulation: II. Dummy Indices Group-theoretic Approach for Symbolic Tensor Manipulation: II. Dummy Indices

2001-07-31

arxiv.org/abs/math-ph/0107032v1

Physics

Mathematical Physics

14 pages, 1 figure, LaTeX

Scientific paper

10.1142/S0129183102004571

Computational Group Theory is applied to indexed objects (tensors, spinors, and so on) with dummy indices. There are two groups to consider: one describes the intrinsic symmetries of the object and the other describes the interchange of names of dummy indices. The problem of finding canonical forms for indexed objects with dummy indices reduces to finding double coset canonical representatives. Well known computational group algorithms are applied to index manipulation, which allow to address the simplification of expressions with hundreds of indices going further to what is needed in practical applications.

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