TFPT scientific source excerpt
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000144 | \begin{definition}[Admissible Schwinger functions]
000145 | \label{def:admissible-schwinger-functions}
000146 | Let
000147 | \[
000148 | W_{\mathrm{rel}}[J,\eta,\bar\eta]:=\log Z_{\mathrm{rel}}[J,\eta,\bar\eta].
000149 | \]
000150 | For local source insertions supported in the Euclidean continuation of
000151 | $\mathcal U_{\mathrm{scat}}$, define the truncated admissible Schwinger distributions by
000152 | \[
000153 | S_n^T(x_1,\ldots,x_n)
000154 | :=
000155 | \left.
000156 | \frac{\delta^n W_{\mathrm{rel}}}{\delta\mathcal J(x_1)\cdots\delta\mathcal J(x_n)}
000157 | \right|_{\mathcal J=0},
000158 | \qquad
000159 | \mathcal J:=(J,\eta,\bar\eta).
000160 | \]