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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2506.10188 |
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| _version_ | 1866914141818585088 |
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| author | Schenk, Sebastian |
| author_facet | Schenk, Sebastian |
| contents | 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 which involve a large number of fields, focussing on massive scalar theories that feature arbitrary self-interactions, $ϕ^{2p}$. Treating quantum fields as operator-valued distributions, we investigate $n$-point correlation functions at ultra-short distances and compute moments and cumulants of fields, using a semiclassical saddle point approximation in the double scaling limit of weak coupling, $λ\to 0$, large quantum number, $n \to \infty$, while keeping $λn$ constant. Addressing the nonperturbative regime, where $λn \gtrsim 1$, 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 $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring Nonperturbative Behaviour of Moments and Cumulants in Quantum Theories Schenk, Sebastian High Energy Physics - Theory High Energy Physics - Phenomenology 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 which involve a large number of fields, focussing on massive scalar theories that feature arbitrary self-interactions, $ϕ^{2p}$. Treating quantum fields as operator-valued distributions, we investigate $n$-point correlation functions at ultra-short distances and compute moments and cumulants of fields, using a semiclassical saddle point approximation in the double scaling limit of weak coupling, $λ\to 0$, large quantum number, $n \to \infty$, while keeping $λn$ constant. Addressing the nonperturbative regime, where $λn \gtrsim 1$, 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 $p$. |
| title | Exploring Nonperturbative Behaviour of Moments and Cumulants in Quantum Theories |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2506.10188 |