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zeta_functions [2015/02/07 15:46] nikolaj |
zeta_functions [2015/02/07 23:43] nikolaj |
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| == traceless part == | == traceless part == | ||
| - | $S=1+T$ | + | $S \equiv 1 + T \equiv 1 - t$ |
| - | + | ||
| - | $S=1-t$ | + | |
| or similar ... here $1$ is the neutral/constant thing in the theory and $T$ resp. $t$ is what's really interesting about $S$. | or similar ... here $1$ is the neutral/constant thing in the theory and $T$ resp. $t$ is what's really interesting about $S$. | ||
| - | E.g. you have a scattering matrix and $1$ is the free propagation and $Y$ is the interaction. | + | E.g. you have a scattering matrix and $1$ is the free propagation and $T$ is the interaction. |
| == Q == | == Q == | ||
| Line 24: | Line 22: | ||
| $Q(S):=\dfrac{1}{1-t}=\sum_{n=0}^\infty t^n$ | $Q(S):=\dfrac{1}{1-t}=\sum_{n=0}^\infty t^n$ | ||
| - | ... flipped linear encoding of $X$ with emphasis on the interesting part. | + | ... flipped linear encoding of $X$ with emphasis on the interesting part. |
| + | |||
| + | It starts out as $Q(S)=1+t+{\marhcal O}(t^2) \approx 1-T$, but it diverges once $t$ reaches $1$. | ||
| - | (and I observe $S\,Q(S)=2\,Q(S)-1$.) | + | (And I observe $S\,Q(S)=2\,Q(S)-1$.) |
| == log == | == log == | ||
