# An Introduction to Tensors and Group Theory for Physicists

@inproceedings{Jeevanjee2011AnIT, title={An Introduction to Tensors and Group Theory for Physicists}, author={Nadir Jeevanjee}, 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.

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## References

SHOWING 1-6 OF 6 REFERENCES

An Introduction to Tensors and Group Theory for Physicists

- Physics
- 2012

JEEVANJEE BOOK. 9780817647148 AN INTRODUCTION TO TENSORS AND GROUP THEORY. AN INTRODUCTION TO TENSORS AND GROUP THEORY FOR PHYSICISTS. AN INTRODUCTION TO TENSORS AND GROUP THEORY FOR PHYSICISTS. AN…

Lie Groups, Lie Algebras, and Representations: An Elementary Introduction

- Mathematics
- 2004

Preface Part I General Theory 1 Matrix Lie Groups 1.1 Definition of a Matrix Lie Group 1.2 Examples of Matrix Lie Groups 1.3 Compactness 1.4 Connectedness 1.5 Simple Connectedness 1.6 Homomorphisms…

Quantum mechanics : a modern development

- Mathematics
- 1998

Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of…

Lectures on Symplectic Geometry, Lecture Notes in Mathematics 1764

- 2001

The Geometry of Physics, 1st ed

- 1997