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First, we point out that the present applied superposition principle islinear, it must be developed into a generality. Next, the linear operators andequations should be developed nonlinearly. They will include nonlinearKlein-Gordon equation and Dirac equations, and corresponding Heisenbergequation. The quantum commutation and anticommutation should be developed. Thistheory may include the renormalization, which is the correction of Feynmanrules of curved closed loops. We think the interaction equations are nonlinear.Many theories, models and phenomena are all nonlinear, for instance, soliton,nonabelian gauge field, and the bag model, etc. The superluminal entangledstate, which relates the nonlocal quantum teleportation and nonlinearity,should be a new fifth interaction. Moreover, the NL effects exist possibly forfour interactions, for single particle, for high energy, and for smallspace-time, etc. The relations among NL theory and electroweak unified theory,and QCD, and CP nonconservation, etc., are expounded. Finally, some known andpossible tests are discussed. The NL theory relates the possible decrease ofentropy in isolated system.

Nonlinear Quantum Theory, Development of the Superposition Principle and Possible Tests