# 電荷共軛宇稱

## 數學形式

${\displaystyle {\mathcal {C}}\,|\psi \rangle =|{\bar {\psi }}\rangle }$

${\displaystyle 1=\langle \psi |\psi \rangle =\langle {\bar {\psi }}|{\bar {\psi }}\rangle =\langle \psi |{\mathcal {C}}^{\dagger }{\mathcal {C}}|\psi \rangle }$

${\displaystyle {\mathcal {C}}{\mathcal {C}}^{\dagger }=\mathbf {1} }$

${\displaystyle {\mathcal {C}}^{2}|\psi \rangle ={\mathcal {C}}|{\bar {\psi }}\rangle =|\psi \rangle }$

${\displaystyle {\mathcal {C}}^{2}=\mathbf {1} }$
${\displaystyle {\mathcal {C}}={\mathcal {C}}^{-1}}$

${\displaystyle {\mathcal {C}}={\mathcal {C}}^{\dagger },}$

### 本徵值與本徵態

${\displaystyle {\mathcal {C}}\,|\psi \rangle =\eta _{C}\,|\psi \rangle }$

${\displaystyle {\mathcal {C}}^{2}|\psi \rangle =\eta _{C}{\mathcal {C}}|{\psi }\rangle =\eta _{C}^{2}|\psi \rangle =|\psi \rangle }$

## 電荷共軛宇稱守恆的實驗驗證

• ${\displaystyle \pi ^{0}\rightarrow 2\gamma }$ ：觀測到中性π介子${\displaystyle \pi ^{0}}$ 會衰變為雙光子γ+γ，因此我們可認定π介子有${\displaystyle \eta _{C}=(-1)^{2}=1}$ 的性質。然而，每增加一個γ會在π介子的電荷共軛宇稱中引入一個-1的因子；衰變成3γ則會違反電荷共軛宇稱守恆。過去曾進行了此種衰變的實驗驗證[1]，其中應用到產生π介子的反應過程：${\displaystyle \pi ^{-}+p\rightarrow \pi ^{0}+n}$
• ${\displaystyle \eta \rightarrow \pi ^{+}\pi ^{-}\pi ^{0}}$ [2]η介子英語Eta meson的衰變。
• ${\displaystyle p{\bar {p}}}$ 湮滅[3]

## 參考文獻

1. ^ MacDonough, J.; et al. Phys. Review. 1988, D38: 2121. 缺少或|title=為空 (幫助)
2. ^ Gormley, M.; et al. Phys. Rev. Lett. 1968, 21: 402. Bibcode:1968PhRvL..21..402G. doi:10.1103/PhysRevLett.21.402. 缺少或|title=為空 (幫助)
3. ^ Baltay, C; et al. Phys. Rev. Lett. 1965, 14: 591. Bibcode:1965PhRvL..14..591R. doi:10.1103/PhysRevLett.14.591. 缺少或|title=為空 (幫助)