狄拉克矩陣

在理論物理學中，狄拉克矩陣$\{\gamma ^{0},\gamma ^{1},\gamma ^{2},\gamma ^{3}\}$，又稱γ矩陣，是狄拉克方程中所引入的四个矩阵，它们是泡利矩阵的推广，满足反对易关系：

$\displaystyle \{\gamma ^{\mu },\gamma ^{\nu }\}=\gamma ^{\mu }\gamma ^{\nu }+\gamma ^{\nu }\gamma ^{\mu }=2\eta ^{\mu \nu }I_{4}$

狄拉克表象四个矩阵：

$\gamma ^{0}={\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}},\quad \gamma ^{1}={\begin{pmatrix}0&0&0&1\\0&0&1&0\\0&-1&0&0\\-1&0&0&0\end{pmatrix}}$

$\gamma ^{2}={\begin{pmatrix}0&0&0&-i\\0&0&i&0\\0&i&0&0\\-i&0&0&0\end{pmatrix}},\quad \gamma ^{3}={\begin{pmatrix}0&0&1&0\\0&0&0&-1\\-1&0&0&0\\0&1&0&0\end{pmatrix}}.$

參考資料

• Halzen, Francis; Martin, Alan. Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons. 1984. ISBN 0-471-88741-2. 
• A. Zee, Quantum Field Theory in a Nutshell (2003), Princeton University Press: Princeton, New Jersey. ISBN 0-691-01019-6. See chapter II.1.
• M. Peskin, D. Schroeder, An Introduction to Quantum Field Theory (Westview Press, 1995) [ISBN 0-201-50397-2] See chapter 3.2.
• W. Pauli. Contributions mathématiques à la théorie des matrices de Dirac. Ann. Inst. Henri Poincaré. 1936, 6: 109.