Log24

(Continued from November 13)

The work of Ron Shaw in this area, ca. 1994-1995, does not
display explicitly the correspondence between anticommutativity
in the set of Dirac matrices and skewness in a line complex of
PG(3,2), the projective 3-space over the 2-element Galois field.

Here is an explicit picture —

References:  

Arfken, George B., Mathematical Methods for Physicists , Third Edition,
Academic Press, 1985, pages 213-214

Cullinane, Steven H., Notes on Groups and Geometry, 1978-1986

Shaw, Ron, "Finite Geometry, Dirac Groups, and the Table of
Real Clifford Algebras," undated article at ResearchGate.net

Update of November 23:

See my post of Nov. 23 on publications by E. M. Bruins
in 1949 and 1959 on Dirac matrices and line geometry,
and on another author who gives some historical background
going back to Eddington.

Some more-recent related material from the Slovak school of
finite geometry and quantum theory —

The matrices underlying the Saniga paper are those of Pauli, not
those of Dirac, but these two sorts of matrices are closely related.

A review of some recent posts on Dirac and geometry,
each of which mentions the late physicist Hendrik van Dam:

• Kummer and Dirac (May 25)
• Framework (May 25)
• Expanding the Spielraum (May 26)
• Dorje (May 26)

The first of these posts mentions the work of E. M. Bruins.
Some earlier posts that cite Bruins:

• Anticommuting Dirac Matrices as Skew Lines (Nov. 20, 2015)
• Dirac and Line Geometry (Nov. 23, 2015)
• Einstein and Geometry (Nov. 27, 2015)