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The operator equations of quantum theory can be replaced formally by functional equations of corresponding Schwinger functionals  1-3 . To give this formalism a physical and mathematical meaning one has to develop a complete functional quantum theory as has been proposed in a preceding paper 4 . Then the complete physical information has to be given by functional operations only. Especially the quantum numbers of ordinary quantum theory have to be reproduced functionally. As the quantum numbers are defined by the eigenvalues of the generators of the corresponding invariance groups, one has to investigate these quantities in functional space. This is done in this paper. To have a definite model we consider the nonlinear spinor field with noncanonical relativistic Heisenberg quantization  5  the form invariance group of which is the Poincare group. Although this model has still other symmetry properties we restrict ourselves to the discussion of the quantum number conditions resulting from this group, as the considerations for other groups and models are quite analogous.

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Symmetry Conditions on Nonlinear Spinor Field Functionals/The symmetry conditions of nonlinear spinor theory of elementary particles, i.e. the definitions of quantum numbers, are given for the nonlinear spinor field functionals.