Relativistic covariance and nonlinear quantum mechanics: Tomonaga-Schwinger analysis

We use the Tomonaga–Schwinger (TS) formulation of quantum field theory to determine when state-dependent additions to the local Hamiltonian density (i.e., modifications to linear Schrödinger evolution) violate relativistic covariance. We derive new operator integrability conditions required for foliation independence, including the Fréchet derivative terms that arise from state-dependence. Nonlinear modifications of quantum mechanics affect operator relations at spacelike separation, leading to violation of the integrability conditions.