标题： 费米子的严格Keldysh泛函积分 显示英文标题

标题： A rigorous Keldysh functional integral for fermions

摘要： 我们为费米子量子场论提供了数学上严格的Keldysh泛函积分。 我们在非常一般的假设下，展示了离散时间Grassmann高斯积分表示在时间连续极限下的收敛性。 我们还证明了有效作用量的解析性，并给出了非平衡系统截断（连通）期望值的显式界。 这些界意味着在热力学极限下具有可求和衰减的聚类性质，前提是这些性质在初始时间成立，并且费米子Keldysh协方差的行列式界和衰减常数在体积上一致有界。 然后我们给出了这些常数的界，并证明对于一类一般的系统，体积的一致性确实成立。 最后我们证明，在耗散量子系统的设定中，这些界不一定仅限于短时间。 显示英文摘要

摘要： 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.