Regularization from Superpositions of Time Evolutions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910231001300992 |
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| author | Aharonov, Yakir Cohen, Eliahu Shushi, Tomer |
| author_facet | Aharonov, Yakir Cohen, Eliahu Shushi, Tomer |
| contents | Short-time approximations and path integrals can be dominated by high-energy or large-field contributions, especially in the presence of singular interactions, motivating regulators that are suppressive yet removable. Standard regulators typically impose such suppressions by hand (e.g. cutoffs, higher-derivative terms, heat-kernel smearing, lattice discretizations), while here we show that closely related smooth filters can arise as the conditional map produced by interference in a coherently controlled, postselected superposition of evolutions. A successful postselection implements a single heralded operator that is a coherent linear combination of time-evolution operators. For a Gaussian superposition of time translations in quantum mechanics, the postselected step is $V_{σ,Δt}=e^{-iHΔt}\,e^{-\frac12σ^2Δt^2H^2}$, i.e.\ the desired unitary step multiplied by a Gaussian energy filter suppressing energies above order $1/(σΔt)$. This renders short-time kernels in time-sliced path-integral approximations well behaved for singular potentials, while the target unitary dynamics is recovered as $σ\to0$ and (for fixed $σ$) also as $Δt\to0$ at fixed $t$. In scalar QFT, a local Gaussian smearing of the quartic coupling induces a positive $(σ^2/2)ϕ^8$ term in the Euclidean action, providing a symmetry-compatible large-field stabilizer; it is naturally viewed as an irrelevant operator whose effects can be renormalized at fixed $σ$ (together with a conventional UV regulator) and removed by taking $σ\to0$. We give short-time error bounds and analyze multi-step success probabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04685 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regularization from Superpositions of Time Evolutions Aharonov, Yakir Cohen, Eliahu Shushi, Tomer Quantum Physics Short-time approximations and path integrals can be dominated by high-energy or large-field contributions, especially in the presence of singular interactions, motivating regulators that are suppressive yet removable. Standard regulators typically impose such suppressions by hand (e.g. cutoffs, higher-derivative terms, heat-kernel smearing, lattice discretizations), while here we show that closely related smooth filters can arise as the conditional map produced by interference in a coherently controlled, postselected superposition of evolutions. A successful postselection implements a single heralded operator that is a coherent linear combination of time-evolution operators. For a Gaussian superposition of time translations in quantum mechanics, the postselected step is $V_{σ,Δt}=e^{-iHΔt}\,e^{-\frac12σ^2Δt^2H^2}$, i.e.\ the desired unitary step multiplied by a Gaussian energy filter suppressing energies above order $1/(σΔt)$. This renders short-time kernels in time-sliced path-integral approximations well behaved for singular potentials, while the target unitary dynamics is recovered as $σ\to0$ and (for fixed $σ$) also as $Δt\to0$ at fixed $t$. In scalar QFT, a local Gaussian smearing of the quartic coupling induces a positive $(σ^2/2)ϕ^8$ term in the Euclidean action, providing a symmetry-compatible large-field stabilizer; it is naturally viewed as an irrelevant operator whose effects can be renormalized at fixed $σ$ (together with a conventional UV regulator) and removed by taking $σ\to0$. We give short-time error bounds and analyze multi-step success probabilities. |
| title | Regularization from Superpositions of Time Evolutions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.04685 |