# nLab Dirac equation

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

The differential equation encoded by a Dirac operator.

The equations of motion of the Dirac field.

## References

The path integral approach to the Dirac equation is discussed in

• Takashi Ichinose?, Hiroshi Tamura?, Path Integral Approach to Relativistic Quantum Mechanics: Two-Dimensional Dirac Equation, Progress of Theoretical Physics Supplement, Volume 92, April 1987, Pages 144–175, doi.

• Pierre Gosselin?, Janos Polonyi?. Path Integral for Relativistic Equations of Motion, arXiv:hep-th/9708121.

• Janos Polonyi?, Path Integral for the Dirac Equation, arXiv:hep-th/9809115.

• Wataru Ichinose?, On the Feynman Path Integral for the Dirac Equation in the General Dimensional Spacetime, Communications in Mathematical Physics 329, 83–508 (2014), doi.

• Wataru Ichinose?, Notes on the Feynman path integral for the Dirac equation, Journal of Pseudo-Differential Operators and Applications 9, 789–809 (2018), doi.

Last revised on January 21, 2021 at 20:42:05. See the history of this page for a list of all contributions to it.