nLab charge conjugation matrix

Idea

In physics, the matrix representing a bilinear form on a real spin representation, i.e. on Majorana spinors is also called the charge conjugation matrix on spinors.

For details see at Majorana spinor – Charge conjugation matrix.

References

• José Figueroa-O'Farrill, p. 12 of Majorana spinors (pdf)

The abstract relation to bilinear forms on spinors is commented on for instance around (3.4) of

• Daniel Freed, Lecture 3 of Five lectures on supersymmetry 1999

and in appendix B.1 of

• Dmitry Vladimirovich Alekseevsky, Vicente Cortez?, C. Devchand, Antoine Van Proeyen, Polyvector Super-Poincaré Algebras Commun.Math.Phys. 253 (2004) 385-422 (arXiv:hep-th/0311107)

The matrix component yoga used in physics is summarized for instance in

• Antoine Van Proeyen, section 3.1 of Tools for supersymmetry (arXiv:hep-th/9910030)

• Joseph Polchinski, volume II, appendix B of String theory

• Friedemann Brandt, section 2.1, 2.3 of Supersymmetry algebra cohomology I: Definition and general structure J. Math. Phys.51:122302, 2010, (arXiv:0911.2118)