- #1

HomogenousCow

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If you calculate the uncertainty of a scalar field in the vacuum state, i.e. ##\langle0\left| \phi^2\right|0\rangle##, you get a divergent integral that comes out to something like

$$\frac{1}{4\pi^2}\int_0^\Lambda \frac{k^2 dk}{\sqrt{{m^2}+{k^2}}}$$

Where ##\Lambda## is some momentum cutoff. How does one make sense of this divergent quantity? Can it be made finite by some "zero-th order" renormalization?

$$\frac{1}{4\pi^2}\int_0^\Lambda \frac{k^2 dk}{\sqrt{{m^2}+{k^2}}}$$

Where ##\Lambda## is some momentum cutoff. How does one make sense of this divergent quantity? Can it be made finite by some "zero-th order" renormalization?

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