Bogolyubov Institute for Theoretical Physics,

14-b Metrologichna Str.,

Kyiv 03143,

UKRAINE

E-mail: mmtpitp@bitp.kiev.ua

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

**Abstract:**

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.