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Generalized wave operators and regularization of perturbation series

V. A. Zhelnorovich


Abstract: All independent complex and real characteristics of a scalar and tensor nature are determined for spinors in $n$-dimensional (generally, complex) Euclidian space. A one-to-one correspondence is established between the components of a spinor and of a proposed special complex tensor aggregate $C$, which is defined by the spinor. In real Euclidian spaces, a homomorphic relation between the components of a spinor and the components of a real tensor aggregate $D$, defined by the spinor, is given. All the formulas and relationships between a spinor and the aggregates $C$ and $D$ are given in particular for four-dimensional Minkowskispace. The resultant theory allows one to arrive at some conclusions about the possibility of a metric description of the interaction between fermion and gravitational fields.

Received: 10.06.1969

 English version: Theoretical and Mathematical Physics, 1970, 2:1, 66–77

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