• Corpus ID: 5503854

This paper is dedicated to the memory of Matey Mateev , a missing friend Clifford Algebras and Spinors

@inproceedings{Todorov2011ThisPI,
  title={This paper is dedicated to the memory of Matey Mateev , a missing friend Clifford Algebras and Spinors},
  author={Ivan Todorov Todorov},
  year={2011}
}

• I. Todorov
• Published 2011
• Mathematics

Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the over twenty-six-year-old Introduction to Majorana masses [1] and includes historical notes and biographical data on past participants in the story. PACS codes: 03.65.Fd, 04.20.Gz 1 Quaternions, Grassmann and Clifford Algebras Clifford’s1 paper [2] on “geometric algebra” (published a year before his death) had two sources: Grassmann’s2 algebra and Hamilton’s3 quaternions whose ∗Lectures presented at the University of Sofia in October-November, 2010. Lecture notes prepared together with Dimitar Nedanovski (e-mail: [e-mail]) and completed during the stay of the author at the ICTP, Trieste and at CERN, Geneva. 1William Kingdon Clifford (1845-1879) early appreciated the work of Lobachevsky and Riemann; he was the first to translate into English Riemann’s inaugural lecture On the hypotheses which lie at the bases of geometry. His view of the physical world as variation of curvature of space anticipated Einstein’s general theory of relativity. He died (before reaching 34) of tuberculosis, aggravated (if not caused) by overwork. 2Hermann Günter Grassmann (1809-1877), a German polymath, first published his fundamental work that led the foundations of linear algebra (and contained the definition of exterior product), in 1844. He was too far ahead of his time to be understood by his contemporaries. Unable to get a position as a professor in mathematics, Grassmann turned to linguistic. His sound law of IndoEuropean (in particular, of Greek and Sanskrit) languages was recognized during his lifetime. 3William Rowan Hamilton (1805-1865) introduced during 1827-1835 what is now called Hamiltonian but also the Lagrangian formalism unifying mechanics and optics. He realized by that time that multiplication by a complex number of absolute value one is equivalent to a rotation in the Euclidean (complex) 2-plane C and started looking for a 3-dimensional generalization of the complex numbers that would play a similar role in the geometry of 3-space. After many unsuccessful attempts, on October 16, 1843, while walking along the Royal Canal, he suddenly had the inspiration that not three but a four dimensional generalization of C existed and was doing the job – see introduction to [3]. 1310–0157 c © 2011 Heron Press Ltd. 3