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Altmann S.L. Icons and Symmetries

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Altmann S.L. Icons and Symmetries
New York: Oxford University Press, 1992. — 114 p.
Ørsted and the principle of symmetry
Physical objects, models, and icons
Archimedes and the balance
Early forms of the principle of conservation of symmetry
The pre-Curie principle of symmetry
Ørsted- and the electromagnetic interaction
The Ørsted paradox
The nature of vectors
The symmetry of vectors
Aquinas, Curie, and the principle of symmetry
Ørsted: no more paradoxes
Archimedes again
130 years after Ørsted: parity non-conservation
Appendix: Ørsted's discovery
Hamilton and rotations
Sir William Rowan Hamilton
Complex numbers
The imaginary unit
An extension of complex numbers: quaternions
Quatemions and rotations
The rectangular transformation
Olinde Rodrigues
Rodrigues and rotations
The rectangular transformation unmasked
The quaternion units
Vectors again
Tensors and spinors
Peierls and symmetry breaking
A little history
The linear chain model
How to deal with translations
Energies and degeneracies
Classification of the energy states
Energy bands in the Brillouin zone
The degeneracy k, -k
The band gap
The Fermi energy
The Peierls instability for the linear chain model
The quasi-linear chain
Bloch functions and degeneracies
The degeneracy introduced by the glide plane
Brillouin zone and bands for the quasi-linear chain
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