Effective non-Hermitian systems with interactions are incompatible with direct inclusion of anti-Hermitian terms in Matsubara Green's functions and are instead described by pseudo-Hermitian quantum mechanics.
The first requirement holds since U (t) is invertible (U (t))− 1 = eiHt , and all invertible functions are bijective
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Physical constraints on effective non-Hermitian systems
Effective non-Hermitian systems with interactions are incompatible with direct inclusion of anti-Hermitian terms in Matsubara Green's functions and are instead described by pseudo-Hermitian quantum mechanics.