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arXiv · 1707.05789

Quantum effective potential from discarded degrees of freedom

Luke M. Butcher
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Abstract

I obtain the quantum correction $ΔV_\mathrm{eff}= (\hbar^2/8m) [(1- 4ξ\frac{d+1}{d})(\mathcal{S}')^2 + 2(1-4ξ)\mathcal{S}"]$ that appears in the effective potential whenever a compact $d$-dimensional subspace (of volume $\propto \exp[\mathcal{S}(x)]$) is discarded from the configuration space of a nonrelativistic particle of mass $m$ and curvature coupling parameter $ξ$. This correction gives rise to a force $-\langleΔV_\mathrm{eff}'\rangle$ that pushes the expectation value $\langle x\rangle$ off its classical trajectory. Because $ΔV_\mathrm{eff}$ does not depend on the details of the discarded subspace, these results constitute a generic model of the quantum effect of discarded variables with maximum entropy/information capacity $\mathcal{S}(x)$.

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Luke M. Butcher. 2018-07-10. Quantum effective potential from discarded degrees of freedom. https://doi.org/10.1016/j.physleta.2018.06.013

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