查看“︁狄拉克矩陣”︁的源代码

{{NoteTA
|G1=物理學
|G2=Math
}}
在[[理論物理學]]中，'''狄拉克矩陣'''<math> \{ \gamma^0, \gamma^1, \gamma^2, \gamma^3 \} </math>，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]]：
::<math>\displaystyle\{ \gamma^\mu, \gamma^\nu \} = \gamma^\mu \gamma^\nu + \gamma^\nu \gamma^\mu = 2 \eta^{\mu \nu} I_4 </math>，其中的上標，依據愛因斯坦求和約定,其為偽標量（不是冪次方的意思）。
狄拉克表象四个矩阵：
:<math> \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} </math>

:<math>\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}.</math>

==參考資料==
* {{cite book | author=Halzen, Francis; Martin, Alan | title=Quarks & Leptons: An Introductory Course in Modern Particle Physics | url=https://archive.org/details/quarksleptonsint0000halz | publisher=John Wiley & Sons | year=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''.
* {{cite journal|author=W. Pauli|journal=Ann. Inst. Henri Poincaré|volume=6|pages=109|year=1936|title=Contributions mathématiques à la théorie des matrices de Dirac|url=http://www.numdam.org/item?id=AIHP_1936__6_2_109_0|access-date=2012-05-06|archive-date=2019-06-29|archive-url=https://web.archive.org/web/20190629120948/http://www.numdam.org/item/?id=AIHP_1936__6_2_109_0|dead-url=no}}

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[[Category:矩陣]]
[[Category:量子场论]]
[[Category:旋量]]