# 手徵對稱性

（重定向自手征对称性

## 量子色動力學範例

${\displaystyle {\mathcal {L}}={\overline {u}}\,i\displaystyle {\not }D\,u+{\overline {d}}\,i\displaystyle {\not }D\,d}$

${\displaystyle \psi _{L}={\frac {1-\gamma ^{5}}{2}}\psi }$
${\displaystyle \psi _{R}={\frac {1+\gamma ^{5}}{2}}\psi }$

${\displaystyle {\mathcal {L}}={\overline {u}}_{L}\,i\displaystyle {\not }D\,u_{L}+{\overline {u}}_{R}\,i\displaystyle {\not }D\,u_{R}+{\overline {d}}_{L}\,i\displaystyle {\not }D\,d_{L}+{\overline {d}}_{R}\,i\displaystyle {\not }D\,d_{R}}$

${\displaystyle q=\left({\begin{matrix}u\\d\end{matrix}}\right)}$

${\displaystyle {\mathcal {L}}={\overline {q}}_{L}\,i\displaystyle {\not }D\,q_{L}+{\overline {q}}_{R}\,i\displaystyle {\not }D\,q_{R}}$

U(1)V變換的方式為

${\displaystyle q_{L}\rightarrow e^{i\theta }q_{L}\qquad q_{R}\rightarrow e^{i\theta }q_{R}}$

U(1)A變換的方式為

${\displaystyle q_{L}\rightarrow e^{i\theta }q_{L}\qquad q_{R}\rightarrow e^{-i\theta }q_{R}}$

## 註釋

1. ^ Griffiths, David J., Introduction to Elementary Particles 2nd revised, WILEY-VCH: pp. 338–342, 2008, ISBN 978-3-527-40601-2
2. ^ Koch, Volker. Aspects of Chiral Symmetry. International Journal Modern Physics. 1997, E6: pp. 203–250.
3. ^ Peskin, Michael; Schroeder, Daniel. An Introduction to Quantum Field Theory. Westview Press. 1995: 670. ISBN 0-201-50397-2.

## 參考文獻

• Walter Greiner and Berndt Müller. Gauge Theory of Weak Interactions. Springer. 2000. ISBN 3-540-67672-4.
• Gordon L. Kane. Modern Elementary Particle Physics. Perseus Books. 1987. ISBN 0-201-11749-5.
• Kondepudi, Dilip K.; Hegstrom, Roger A. The Handedness of the Universe. Scientific American. January 1990, 262 (1): 108–115.
• Winters, Jeffrey. Looking for the Right Hand. Discover. November 1995 [12 September 2015].