# nLab Dirac field

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, specifically in field theory, a Dirac field is an electromagentially charged and possibly massive a fermionic spinor field.

This includes fermions in the standard model of particle physics, such as electrons, quarks, neutrinos and muons, after the Higgs mechanism has equipped them with mass.

Mathematically, the Dirac field is the field whose field bundle is a spinor bundle with typical fiber a Dirac representation in odd super-degree and whose equation of motion is a Dirac equation.

Notice that there are other spinor fields which would not be called “Dirac fields”, such as those transforming in a Majorana representation or a Weyl representation, or for example the gravitino field which would be called a Rarita-Schwinger field.

## Reference

A concise collection of the details over Minkowski spacetime is in

with background on spinor fields in

A textbook account in the context of causal perturbation theory is in

Last revised on January 20, 2018 at 11:29:36. See the history of this page for a list of all contributions to it.