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Exploring nonperturbative behavior of moments and cumulants in quantum theories

Sebastian Schenk

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Phys. Rev. D 112, 096018 – Published 17 November, 2025

DOI: https://doi.org/10.1103/1v5p-byjf

Abstract

The dynamics of quantum fields become nonperturbative when their interactions are probed by a large number of particles. To explore this regime, we study correlation functions that involve a large number of fields, focusing on massive scalar theories that feature arbitrary self-interactions, ϕ2p. Treating quantum fields as operator-valued distributions, we investigate n-point correlation functions at ultrashort distances and compute moments and cumulants of fields, using a semiclassical saddle point approximation in the double scaling limit of weak coupling, λ→0, large quantum number, n→∞, while keeping λn constant. Addressing the nonperturbative regime, where λn≳1, requires a resummation of the effective saddle point to all orders in λn. We perform this resummation in zero and one dimensions and show that the moments, corresponding to correlation functions including disconnected contributions, grow exponentially with n. This growth is significantly reduced for higher-order self-interactions, i.e., for larger p. On the other hand, we argue that the cumulants, which represent connected correlation functions, grow even more rapidly and are mostly independent of p.

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Phys. Rev. D 112, 096018– Published 17 November, 2025
  • Received 27 June 2025
  • Accepted 29 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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