= Scalar potential from a field-dependent momentum cutoff
{title2=$V(\varphi)=\frac1{4\pi^2}\int_0^{|\varphi|}p^2\sqrt{p^2+m^2}\,dp$}
If a free real <scalar field>'s three-<momentum> <ultraviolet cutoff> is identified with the absolute <vacuum expectation value> of another <scalar field>, the displayed <scalar potential> is even and has its unique <global minimum> at zero. It grows as $\varphi^4/(16\pi^2)$ for $|\varphi|\gg m$, but as $m|\varphi|^3/(12\pi^2)$ for $|\varphi|\ll m$ with $m>0$. The positive derivative with respect to $|\varphi|$ proves that this contribution alone does not produce <spontaneous symmetry breaking>. This cutoff identification is a model assumption, distinct from deriving a complete <effective potential> for a dynamical <field>.
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