A rigorous Keldysh functional integral for fermions
We provide a mathematically rigorous Keldysh functional integral for fermionic quantum field theories. We show convergence of a discrete-time Grassmann Gaussian integral representation in the time-continuum limit under very general hypotheses. We also prove analyticity of the effective action and ex...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
14 February 2026
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| In: |
Journal of statistical physics
Year: 2026, Volume: 193, Issue: 2, Pages: 1-20 |
| ISSN: | 1572-9613 |
| DOI: | 10.1007/s10955-026-03583-5 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s10955-026-03583-5
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| Author Notes: | Philipp Benjamin Aretz, Manfred Salmhofer |
| Summary: | We provide a mathematically rigorous Keldysh functional integral for fermionic quantum field theories. We show convergence of a discrete-time Grassmann Gaussian integral representation in the time-continuum limit under very general hypotheses. We also prove analyticity of the effective action and explicit bounds for the truncated (connected) expectation values $$\gamma ^\textrm{c}_{m,\bar{m}}$$of the non-equilibrium system. These bounds imply clustering with a summable decay in the thermodynamic limit, provided these properties hold at time zero, and provided that the determinant bound $$\delta _C$$and decay constant $$\alpha _C$$of the fermionic Keldysh covariance are bounded uniformly in the volume. We then give bounds for these constants and show that uniformity in the volume indeed holds for a general class of systems. Finally we show that in the setting of dissipative quantum systems, these bounds are not necessarily restricted to short times. |
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| Item Description: | Gesehen am 22.05.2026 |
| Physical Description: | Online Resource |
| ISSN: | 1572-9613 |
| DOI: | 10.1007/s10955-026-03583-5 |