# nLab charge conjugation matrix

Contents

## Spin geometry

spin geometry

Dynkin labelsp. orth. groupspin grouppin groupsemi-spin group
SO(2)Spin(2)Pin(2)
B1SO(3)Spin(3)Pin(3)
D2SO(4)Spin(4)Pin(4)
B2SO(5)Spin(5)Pin(5)
D3SO(6)Spin(6)
B3SO(7)Spin(7)
D4SO(8)Spin(8)SO(8)
B4SO(9)Spin(9)
D5SO(10)Spin(10)
B5SO(11)Spin(11)
D6SO(12)Spin(12)
$\vdots$$\vdots$
D8SO(16)Spin(16)SemiSpin(16)
$\vdots$$\vdots$
D16SO(32)Spin(32)SemiSpin(32)

string geometry

# Contents

## 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

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

and in appendix B.1 of

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

Last revised on April 2, 2019 at 14:41:50. See the history of this page for a list of all contributions to it.