式の纏め方につきまして

式の纏め方につきまして

cat さんの書込 (2008/05/28(Wed) 23:32)

こんにちは

式をどのように纏めて表現すれば良いのか？困っています． 次の式を纏めると

m^2 &= ({\gamma^0}{p^{0}})^2+({\gamma^1}{p^{1}})^2+({\gamma^2}{p^{2}})^2+({\gamma^3}p^{3})^2 \nonumber \\ %&+ 2({(\pi^1)^2-(\lambda^1)^2}) {p^{0}}{p^{1}}+ 2({(\pi^2)^2-(\lambda^2)^2}) {p^{0}}{p^{2}}+ 2({(\pi^3)^2-(\lambda^3)^2}){p^{0}}{p^{3}} \nonumber \\ &+ 2({(\pi^4)^2-(\lambda^4)^2}) {p^{1}}{p^{2}}+ 2({(\pi^5)^2-(\lambda^5)^2}) {p^{2}}{p^{3}}+ 2({(\pi^6)^2-(\lambda^6)^2}){p^{1}}{p^{3}} \nonumber \\%&+(\gamma^1 \gamma^2+\gamma^2 \gamma^1) p^{1} p^{2} +(\gamma^2 \gamma^3+\gamma^3 \gamma^2) p^{2} p^{3}+(\gamma^3 \gamma^1+\gamma^1 \gamma^3) p^{3} p^{1} \nonumber \\&+(\gamma^0 \gamma^1+\gamma^1 \gamma^0) p^{0} p^{1}+(\gamma^0 \gamma^2+\gamma^2 \gamma^0) p^{0}p^{2}+(\gamma^0 \gamma^3+\gamma^3 \gamma^0) p^{0} p^{3}\nonumber \\%&+\sqrt{2}(\gamma^0 (\pi^1+i\lambda^1)+ (\pi^1+i\lambda^1) \gamma^0) p^{0}\sqrt{p^{0} p^{1}}+\sqrt{2}(\gamma^0 (\pi^2+i\lambda^2) + (\pi^2+i\lambda^2) \gamma^0) p^{0}\sqrt{p^{0} p^{2}}\nonumber \\&+\sqrt{2}(\gamma^0 (\pi^3+i\lambda^3)+ (\pi^3+i\lambda^3) \gamma^0) p^{0}\sqrt{p^{0} p^{3}}+\sqrt{2}(\gamma^0 (\pi^4+i\lambda^4) + (\pi^4+i\lambda^4) \gamma^0) p^{0}\sqrt{p^{1} p^{2}}\nonumber \\&+\sqrt{2}(\gamma^0 (\pi^5+i\lambda^5)+ (\pi^5+i\lambda^5) \gamma^0) p^{0}\sqrt{p^{2} p^{3}}+\sqrt{2}(\gamma^0 (\pi^6+i\lambda^6) + (\pi^6+i\lambda^6) \gamma^0) p^{0}\sqrt{p^{1} p^{3}}\nonumber \\%&+\sqrt{2}(\gamma^1 (\pi^1+i\lambda^1)+ (\pi^1+i\lambda^1) \gamma^1) p^{1}\sqrt{p^{0} p^{1}}+\sqrt{2}(\gamma^1 (\pi^2+i\lambda^2) + (\pi^2+i\lambda^2) \gamma^1) p^{1}\sqrt{p^{0} p^{2}}\nonumber \\&+\sqrt{2}(\gamma^1 (\pi^3+i\lambda^3)+ (\pi^3+i\lambda^3) \gamma^1) p^{1}\sqrt{p^{0} p^{3}}+\sqrt{2}(\gamma^1 (\pi^4+i\lambda^4) + (\pi^4+i\lambda^4) \gamma^1) p^{1}\sqrt{p^{1} p^{2}}\nonumber \\&+\sqrt{2}(\gamma^1 (\pi^5+i\lambda^5)+ (\pi^5+i\lambda^5) \gamma^1) p^{1}\sqrt{p^{2} p^{3}}+\sqrt{2}(\gamma^1 (\pi^6+i\lambda^6) + (\pi^6+i\lambda^6) \gamma^1) p^{1}\sqrt{p^{1} p^{3}}\nonumber \\%&+\sqrt{2}(\gamma^2 (\pi^1+i\lambda^1)+ (\pi^1+i\lambda^1) \gamma^2) p^{2}\sqrt{p^{0} p^{1}}+\sqrt{2}(\gamma^2 (\pi^2+i\lambda^2) + (\pi^2+i\lambda^2) \gamma^2) p^{2}\sqrt{p^{0} p^{2}}\nonumber \\&+\sqrt{2}(\gamma^2 (\pi^3+i\lambda^3)+ (\pi^3+i\lambda^3) \gamma^2) p^{2}\sqrt{p^{0} p^{3}}+\sqrt{2}(\gamma^2 (\pi^4+i\lambda^4) + (\pi^4+i\lambda^4) \gamma^2) p^{2}\sqrt{p^{1} p^{2}}\nonumber \\&+\sqrt{2}(\gamma^2 (\pi^5+i\lambda^5)+ (\pi^5+i\lambda^5) \gamma^2) p^{2}\sqrt{p^{2} p^{3}}+\sqrt{2}(\gamma^2 (\pi^6+i\lambda^6) + (\pi^6+i\lambda^6) \gamma^2) p^{2}\sqrt{p^{1} p^{3}}\nonumber \\%&+\sqrt{2}(\gamma^3 (\pi^1+i\lambda^1)+ (\pi^1+i\lambda^1) \gamma^3) p^{3}\sqrt{p^{0} p^{1}}+\sqrt{2}(\gamma^3 (\pi^2+i\lambda^2) + (\pi^2+i\lambda^2) \gamma^3) p^{3}\sqrt{p^{0} p^{2}}\nonumber \\&+\sqrt{2}(\gamma^3 (\pi^3+i\lambda^3)+ (\pi^3+i\lambda^3) \gamma^3) p^{3}\sqrt{p^{0} p^{3}}+\sqrt{2}(\gamma^3 (\pi^4+i\lambda^4) + (\pi^4+i\lambda^4) \gamma^3) p^{3}\sqrt{p^{1} p^{2}}\nonumber \\&+\sqrt{2}(\gamma^3 (\pi^5+i\lambda^5)+ (\pi^5+i\lambda^5) \gamma^3) p^{3}\sqrt{p^{2} p^{3}}+\sqrt{2}(\gamma^3 (\pi^6+i\lambda^6) + (\pi^6+i\lambda^6) \gamma^3) p^{3}\sqrt{p^{1} p^{3}}\nonumber \\%&+2((\pi^1+i\lambda^1) (\pi^2+i\lambda^2)+ (\pi^2+i\lambda^2) (\pi^1+i\lambda^1))\sqrt{(p^{0})^2p^{1}p^{2}}\nonumber \\&+2((\pi^1+i\lambda^1) (\pi^3+i\lambda^3)+ (\pi^3+i\lambda^3) (\pi^1+i\lambda^1))\sqrt{(p^{0})^2p^{1}p^{3}}\nonumber \\&+2((\pi^2+i\lambda^2) (\pi^3+i\lambda^3)+ (\pi^3+i\lambda^3) (\pi^2+i\lambda^2))\sqrt{(p^{0})^2p^{2}p^{3}}\nonumber \\&+2((\pi^1+i\lambda^1) (\pi^4+i\lambda^4)+ (\pi^4+i\lambda^4) (\pi^1+i\lambda^1))\sqrt{p^{0}(p^{1})^2p^{3}}\nonumber \\&+2((\pi^2+i\lambda^2) (\pi^4+i\lambda^4)+ (\pi^4+i\lambda^4) (\pi^2+i\lambda^2))\sqrt{p^{0}p^{1}(p^{2})^2}\nonumber \\&+2((\pi^3+i\lambda^3) (\pi^4+i\lambda^4)+ (\pi^4+i\lambda^4) (\pi^3+i\lambda^3))\sqrt{p^{0}p^{1}p^{2}p^{3}}\nonumber \\&+2((\pi^1+i\lambda^1) (\pi^5+i\lambda^5)+ (\pi^5+i\lambda^5) (\pi^1+i\lambda^1))\sqrt{p^{0}p^{1}p^{2}p^{3}}\nonumber \\&+2((\pi^2+i\lambda^2) (\pi^5+i\lambda^5)+ (\pi^5+i\lambda^5) (\pi^2+i\lambda^2))\sqrt{p^{0}(p^{2})^2p^{3}}\nonumber \\&+2((\pi^3+i\lambda^3) (\pi^5+i\lambda^5)+ (\pi^5+i\lambda^5) (\pi^3+i\lambda^3))\sqrt{p^{0}p^{2}(p^{3})^2}\nonumber \\&+2((\pi^4+i\lambda^4) (\pi^5+i\lambda^5)+ (\pi^5+i\lambda^5) (\pi^4+i\lambda^4))\sqrt{p^{1}(p^{2})^2p^{3}}\nonumber \\&+2((\pi^1+i\lambda^1) (\pi^6+i\lambda^6)+ (\pi^6+i\lambda^6) (\pi^1+i\lambda^1))\sqrt{p^{0}(p^{1})^2p^{3}}\nonumber \\&+2((\pi^2+i\lambda^2) (\pi^6+i\lambda^6)+ (\pi^6+i\lambda^6) (\pi^2+i\lambda^2))\sqrt{p^{0}p^{1}p^{2}p^{3}}\nonumber \\&+2((\pi^3+i\lambda^3) (\pi^6+i\lambda^6)+ (\pi^6+i\lambda^6) (\pi^3+i\lambda^3))\sqrt{p^{0}p^{1}(p^{3})^2}\nonumber \\&+2((\pi^4+i\lambda^4) (\pi^6+i\lambda^6)+ (\pi^6+i\lambda^6) (\pi^4+i\lambda^4))\sqrt{(p^{1})^2 p^{2}p^{3}}\nonumber \\&+2((\pi^5+i\lambda^5) (\pi^6+i\lambda^6)+ (\pi^6+i\lambda^6) (\pi^5+i\lambda^5))\sqrt{p^{1}p^{2}(p^{3})^2}

下記でよろしいでしょうか？

m^2 &= (\gamma^0 p^0)^2+\sum_{i}(\gamma^i p^i)^2+2 \sum_{i \neq j} (({\pi^i})^2-({\lambda^i})^2) p^\mu p^\nu \nonumber \\&+\sum_{i\neq j}(\gamma^i \gamma^j+\gamma^j \gamma^i)p^ip^j+\sqrt{2} \sum_{i \neq j}(\gamma^i (\pi^j+i \lambda^j)+ (\pi^j+i \lambda^j)\gamma^i)p^i \sqrt{p^\mu p^\nu}\nonumber \\&+2\sum_{i\neq j}((\pi^i+i\lambda^i) (\pi^j+i\lambda^j)+ (\pi^j+i\lambda^j) (\pi^i+i\lambda^i))\sqrt{p^{\mu}p^{\nu}p^{\alpha}p^{\beta}}\label{eq:eq306}

Re: 式の纏め方につきまして

toorisugari no Hiro さんのレス (2008/05/29(Thu) 11:40)

まず，ぱっと見． \sqrt{p^\mu p^\mu} などの添え字が変ですね．

あと見づらいので暫定的に上付き添え字を下付き添え字に変えてください．(べきと区別してください)