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extended_quantum_action_functional_._finite [2015/01/30 12:55]
nikolaj
extended_quantum_action_functional_._finite [2015/08/25 23:14]
nikolaj
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 | @#FFBB00: definiendum | @#FFBB00: $Z:(\mathbb K^2\to\mathbb R)\to \mathbb K^4\to \mathbb K $ | | @#FFBB00: definiendum | @#FFBB00: $Z:(\mathbb K^2\to\mathbb R)\to \mathbb K^4\to \mathbb K $ |
 | @#FFBB00: definiendum | @#FFBB00: $Z_{\mathcal L_\mathrm{int}}(J,​K,​\phi,​\psi):​=\mathrm{e}^{i\hbar^{-1}\sum_{i=1}^m\mathcal L_\mathrm{int}\left(-i\,​\hbar\frac{\partial}{\partial J_i},​-i\,​\hbar\frac{\partial}{\partial K_i}\right)} \left( \mathrm{e}^{i\,​\hbar^{-1} \left\langle J\left|\,​\mathcal{R}_\varepsilon\,​\right|K\right\rangle}\cdot\mathrm{e}^{Z_\text{source}(J,​K,​\phi,​\psi)}\right)$ | | @#FFBB00: definiendum | @#FFBB00: $Z_{\mathcal L_\mathrm{int}}(J,​K,​\phi,​\psi):​=\mathrm{e}^{i\hbar^{-1}\sum_{i=1}^m\mathcal L_\mathrm{int}\left(-i\,​\hbar\frac{\partial}{\partial J_i},​-i\,​\hbar\frac{\partial}{\partial K_i}\right)} \left( \mathrm{e}^{i\,​\hbar^{-1} \left\langle J\left|\,​\mathcal{R}_\varepsilon\,​\right|K\right\rangle}\cdot\mathrm{e}^{Z_\text{source}(J,​K,​\phi,​\psi)}\right)$ |
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 | @#BBDDEE: $\mathcal{R}_\varepsilon\equiv-\left(D+i\,​\varepsilon\,​\mathrm{1}\right)^{-1}$ | | @#BBDDEE: $\mathcal{R}_\varepsilon\equiv-\left(D+i\,​\varepsilon\,​\mathrm{1}\right)^{-1}$ |
 | @#BBDDEE: $Z_\text{source}(J,​K,​\phi,​\psi):​=i\,​\hbar^{-1}\left(\left\langle J\left|\right. \phi\right\rangle+\left\langle K\left|\right. \psi\right\rangle\right)$ | | @#BBDDEE: $Z_\text{source}(J,​K,​\phi,​\psi):​=i\,​\hbar^{-1}\left(\left\langle J\left|\right. \phi\right\rangle+\left\langle K\left|\right. \psi\right\rangle\right)$ |
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