Tensors

Nadir Jeevanjee
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Nadir Jeevanjee: University of California at Berkeley, Department of Physics

Chapter Chapter 3 in An Introduction to Tensors and Group Theory for Physicists, 2015, pp 51-105 from Springer

Abstract: Abstract This chapter begins with the abstract, coordinate-free definition of a tensor. This definition is standard in the math literature and in texts on General Relativity, but is otherwise not accessible in the physics literature. A major feature of this book is that it provides a relatively quick route to this definition, without the full machinery of differential geometry and tensor analysis. After the definition and some examples we thoroughly discuss change of bases and make contact with the usual coordinate-dependent definition of tensors. Matrix equations for a change of basis are also given. This is followed by a discussion of active and passive transformations. We then define the tensor product and uncover many applications of tensor products in classical and quantum physics. We close with a discussion of symmetric and anti-symmetric tensors, with examples concerning determinants and pseudovectors. The connection between anti-symmetric tensors and rotations is made, which leads naturally to the subject of Lie Groups and Lie Algebras in Part II.

Keywords: Anti-symmetric Tensor; Passive Transformation; Pseudovector; Dual Vector; Bivector (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-14794-9_3

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DOI: 10.1007/978-3-319-14794-9_3

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