An Introduction to Tensors and Group Theory for Physicists

@inproceedings{Jeevanjee2011AnIT,
title={An Introduction to Tensors and Group Theory for Physicists},
year={2011}
}
Part I Linear Algebra and Tensors.- A Quick Introduction to Tensors.- Vector Spaces.- Tensors.- Part II Group Theory.- Groups, Lie Groups, and Lie Algebras.- Basic Representation Theory.- The Winger-Echart Theorem and Other Applications.- Appendix Complexifications of Real Lie Algebras and the Tensor Product Decomposition of sl(2,C)R.- References.- Index.
28 Citations
The Poor Man ’ s Introduction to Tensors
When solving physical problems, one must often choose between writing formulas in a coordinate independent form or a form in which calculations are transparent. Tensors are important because they
Signatures of Stable Multiplicity Spaces in Restrictions of Representations of Symmetric Groups
Representation theory is a way of studying complex mathematical structures such as groups and algebras by mapping them to linear actions on vector spaces. Recently, Deligne proposed a new way to
Representation of Material Properties by Means of Cartesian Tensors
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The goal of this chapter is to familiarize the reader with the basic ideas and the few manipulation rules for Cartesian tensors [1, 2, 3, 4, 5, 6] that will be required in the rest of the book. If
Compact construction algorithms for the singlets of SU(N) over mixed tensor product spaces.
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The irreducible representations of SU(N) over a mixed quark-antiquark Fock space component have been studied for many years. In analogy to the case for the quark-only Fock space component, there
Selected Solutions for An Introduction to Tensors and Group Theory for Physicists, 2nd ed
• 2020
This is an incomplete, evolving solutions manual to [Jee15]. Note that this is the second edition of this text, and that exercise and problem numbering differs between editions. Solutions posted here
Wigner-Eckart theorem for the non-compact algebra sl(2,R)
The Wigner-Eckart theorem is a well known result for tensor operators of su(2) and, more generally, any compact Lie algebra. In this paper the theorem will be generalized to the particular
Vectors, Vector Calculus, and Coordinate Systems
Physical laws and coordinate systems For the present discussion, we define a “coordinate system” as a system for describing positions in space. Coordinate systems are human inventions, and therefore
Demystifying Tensors: a Friendly Approach for Students of All Disciplines
This paper argues that the geometric approach to tensors is the more pedagogically correct of the two, for tensors of all ranks, and encourages other instructors to adopt this approach in their own courses.
Properties of a class of generalized Freud polynomials
Semiclassical orthogonal polynomials are polynomials orthogonal with respect to semiclassical weights. The fascinating link between semiclassical orthogonal polynomials and discrete integrable
Material Tensors and Pseudotensors of Weakly-Textured Polycrystals with Orientation Measure Defined on the Orthogonal Group
OF DISSERTATION MATERIAL TENSORS AND PSEUDOTENSORS OF WEAKLY-TEXTURED POLYCRYSTALS WITH ORIENTATION MEASURE DEFINED ON THE ORTHOGONAL GROUP Material properties of polycrystalline aggregates should