Showing papers on "Higher-dimensional supergravity published in 1970"

Gauge-invariant spinor theories

Abstract: It is demonstrated that in spinor theories with nonlinear quadratic self-interaction, gauge symmetries connected withx-dependent internal symmetry transformations can be established without the introduction of additional vector fields if the spinor field operator has the noncanonical length dimension −1/2. In this case the theory is scale invariant at small distances and hence formally renormalizable. Operator products can be defined according to prescriptions given by Zimmermann and Wilson. The usual role of the gauge fields in these spinor theories is taken over by the formally constructed vector and axial vector «currents» of the noncanonical spinor fields which have the correct length dimension of boson operators. Physical fermion fields are related to deverivatives of these spinor fields or to 3-products of these fields. The noncanonical spinor field hence may be regarded as a «spinor potential» in the sense that its relation to a physical spinor field is similar to the relation of the vector potential to the physical electromagnetic field. The unobservable «spinor potential» acts in a state space with indefinite metric. Examples forSU n ⊗SU n gauge-invariant theories are given. The Heisenberg nonlinear spinor theory is shown to beSU 2 gauge-invariant, and hence the parity symmetry version of Durr to beSU 2⊗SU 2 gauge-invariant. This formal invariance, however, does not necessarily imply that the summetry holds in Hilbert space.

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.

Abstract: 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 paper4. 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.