Quantum effective potential from discarded degrees of freedom

Abstract

I obtain the quantum correction $\Delta V_{\mathrm{eff}}=({\hslash }^2/8m)[(1-4\xi \frac{d+1}{d})({\mathcal{S}}^{\prime }{)}^2+2(1-4\xi )\mathcal{S}"]$ 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 $\xi$. This correction gives rise to a force $-⟨\Delta V_{\mathrm{eff}}^{\prime }⟩$ that pushes the expectation value $⟨x⟩$ off its classical trajectory. Because $\Delta V_{\mathrm{eff}}$ 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 $\mathcal{S}(x)$.

7 pages, 1 figure; published version with appendix

References in corpus (1)

• Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space

Cited by in corpus (3)

• New physics in light of the $H_0$ tension: an alternative view
• Quantum Bias Cosmology: Acceleration from Holographic Information Capacity
• Path integrals with discarded degrees of freedom