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[1] Werner S A 1980 Phys. Today 33 24

[2] Rauch H et al 1975 Phys. Lett. 54A 425

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¹It should be noted that rotations in (3, R) can be elegantly represented using quaternions. Use of quaternions avoids gimbal lock; they are used for programming robots and computer games.

²The notation σ⃗, i.e. (σx,σy,σz), viewed as a vector when the components are matrices, needs to be adopted as a powerful language. This will lead to the concept of vector operators in chapter 3; therein, the concept is formally developed. (See also Volume 1, equation (7.72).)

³The measure of a space appears in the infinitesimal volumes under integrals. For example, polar coordinates in three dimensions possess an infinitesimal volume expressed as r2drsinθdθdϕ and the measure is r2sinθ. Cartesian coordinates possess a trivial measure because the infinitesimal volume under an integral is dxdydz (this space could be said to be ‘flat’).