Year: 2026
Type: article
Abstract: 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 $$\gamma ^\textrm{c}_{m,\bar{m}}$$ γ m , m ¯ c 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 $$\delta _C$$ δ C and decay constant $$\alpha _C$$ α 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.
Source: Journal of Statistical Physics
Authors: Philipp Benjamin Aretz, Manfred Salmhofer
Institution: Heidelberg University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7128924640