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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: $Z_\text{source}(J,K,\phi,\psi):=i\,\hbar^{-1}\left(\left\langle J\left|\right. \phi\right\rangle+\left\langle K\left|\right. \psi\right\rangle\right)$ | |