Bogolyubov Institute for Theoretical Physics,
14-b Metrologichna Str.,
Kyiv 03143,

Symmetries and quantum anomalies of composite fields in the Heisenberg approach to the Universe

Manifestation of symmetries and quantum anomalies of composite fields is demonstrated as striking correlations between properties of scalar, pseudoscalar, vector, and pseudovector composite fields which are constituted from quantum spinor fields in any space-time dimension $n=2r_n+\delta_n$, $r_n=0,1,2,\ldots$,   $\delta_n=0,1$. The consideration is carried out in the framework of the self-consistent renormalization for $n$-dimensional quantum spinor field models in which mass spectrum of many-fermion sector may be both degenerate and nondegenerate. The distinction between the chiral case and the the chiral limit case is investigated as well.