Relativistic Covariance and Nonlinear Quantum Mechanics: Tomonaga-Schwinger Analysis

TL;DR

This paper investigates how nonlinear modifications to quantum mechanics impact relativistic covariance using the Tomonaga-Schwinger formulation, deriving conditions for foliation independence and showing that nonlinearity can violate these conditions.

Contribution

It introduces new operator integrability conditions for state-dependent Hamiltonian modifications and analyzes their implications for relativistic covariance.

Findings

Nonlinear quantum modifications can violate foliation independence.

New operator integrability conditions are derived for relativistic covariance.

State-dependence affects operator relations at spacelike separation.

Abstract

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 Schrodinger evolution) violate relativistic covariance. We derive new operator integrability conditions required for foliation independence, including the Frechet 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.