A rigorous Keldysh functional integral for fermions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913973056569344 |
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| author | Aretz, Philipp Benjamin Salmhofer, Manfred |
| author_facet | Aretz, Philipp Benjamin Salmhofer, Manfred |
| contents | 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 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 and decay constant 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_01787 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A rigorous Keldysh functional integral for fermions Aretz, Philipp Benjamin Salmhofer, Manfred Mathematical Physics Strongly Correlated Electrons 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 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 and decay constant 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. |
| title | A rigorous Keldysh functional integral for fermions |
| topic | Mathematical Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2508.01787 |