Definition: Total Angular Momentum Vector
Noun Definition
Total Angular Momentum Vector $\begin{align} &\ \ \ \ \ \ \ \ \ \ \ \ {\rm{\overline{J}}} \equiv \left( {\rm{J}}_{m} , \ {\rm{J}}_{e} , \ {\rm{J}}_{z} \right) \ \ \ \ \ \ \sf{\text{where}} \\ \ \\ \ \\ {\rm{J}}_{m} &\equiv \delta _{\hat{m}} \frac{h}{\mathrm{16} \pi} \sqrt{ \left( N^{\mathsf{A}}-N^{\mathsf{M}} \right)^{2} + 8 \, {\large{\mid}} N^{\mathsf{A}}-N^{\mathsf{M}} {\large{\mid}} \; } \\ \ \\ \ \\ {\rm{J}}_{e} &\equiv \delta _{\hat{e}} \frac{h}{\mathrm{16} \pi} \sqrt{ \left( N^{\mathsf{G}}-N^{\mathsf{E}} \right)^{2} + 8 \, {\large{\mid}} N^{\mathsf{G}}-N^{\mathsf{E}} {\large{\mid}} \; } \\ \ \\ \ \\ {\rm{J}}_{z} &\equiv \delta _{z} \frac{h}{\mathrm{16} \pi} \sqrt{ \left( N^{\mathsf{U}}-N^{\mathsf{D}} \right)^{2} + 8 \, {\large{\mid}} N^{\mathsf{U}}-N^{\mathsf{D}} {\large{\mid}} \; } \end{align}$ 5-40

Logical Antecedents

Adjectives Definition
Quark Coefficients $n \ \ {\sf{\text{and}}} \ \ N \ \ \sf{\text{count the number of quarks in a particle}}$ 4-3
Adjective Definition
Helicity $\delta _{z} \equiv \begin{cases} +1 \ \ &\sf{\text{if}} \ \ &N^{\mathsf{U}} \ > \ N^{\mathsf{D}} \\ \ \ 0 \ \ &\sf{\text{if}} \ \ &N^{\mathsf{U}} \ = \, N^{\mathsf{D}} \\ -1 \ \ &\sf{\text{if}} \ \ &N^{\mathsf{U}} \ < \ N^{\mathsf{D}} \end{cases}$ 5-38
Adjective Definition
Magnetic Polarity $\delta _{\hat{m}} \equiv \begin{cases} +1 \ \ &\sf{\text{if}} \ \ &\it{N}^{\, \mathsf{M}} > \it{N}^{\, \mathsf{A}} \\ \ \ 0 \ \ &\sf{\text{if}} \ \ &\it{N}^{\, \mathsf{M}} \ \sf{=} \ \, \it{N}^{\, \mathsf{A}} \\ -1 \ \ &\sf{\text{if}} \ \ &\it{N}^{\, \mathsf{M}} < \it{N}^{\, \mathsf{A}} \end{cases}$ 5-35
Adjective Definition
Electric Polarity $\delta _{\hat{e}} \equiv \begin{cases} +1 \ \ &\sf{\text{if}} \ \ &\it{N}^{\, \mathsf{G}} > \it{N}^{\, \mathsf{E}} \\ \ \ 0 \ \ &\sf{\text{if}} \ \ &\it{N}^{\, \mathsf{G}} \ \sf{=} \ \, \it{N}^{\, \mathsf{E}} \\ -1 \ \ &\sf{\text{if}} \ \ &\it{N}^{\, \mathsf{G}} < \it{N}^{\, \mathsf{E}} \end{cases}$ 5-36

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