When Hamilton had invented quaternions, the question arose whether they could be used to advantage in mathematical physics. However, the world then only had three dimensions, and so the scalar part of the quaternion was suppressed, the resulting entity being called a vector. The relation between vector-analysis and quaternion algebra is well known, and need not be entered into here. With the theory of relativity also came the fourth dimension. Although Minkowski himself rejected the quaternionic calculus as “too narrow and clumsy for the purpose in question”, Silberstein has strongly advocated the cause of quaternions. He used quaternions with imaginary scalar parts to designate the position of points or events in space-time. This was necessary, since the metric in Minkowski space is not given by a positive definite quadratic form. We achieve the same result by making the vector part imaginary, in which case we obtain a Hermitian matrix representation of the position quaternion. Professor Dirac believes (as stated by him in conversation) that, some day, Hamiltonian quaternions, as opposed to Hermitian quaternions, will re-assert themselves in relativity theory; but I do not see how this can be. [...]
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.104060 |
| Date | January 1950 |
| Creators | Lambek, Joachim |
| Contributors | Coxeter, H.S.M. (Supervisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mathematics) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: NNNNNNNNN, Theses scanned by McGill Library. |
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