  In this work, we introduce some new $U(1)$ symmetry groups of the free
fermionic action in euclidean space-time, which are a consequence of parity and
time-reversal symmetries. Afterwards, we discuss how the introduction of a
gauge interaction affects the invariance of the action, with special reference
to QCD. Moreover, inspired by recent QCD lattice results of \textit{Glozman et
al.}, in which an interesting and unexpected symmetry group has been observed,
namely $SU(2)_{CS}$ (that contains $U(1)_A$ as subgroup), we build other
$SU(2)_{CS}$-like groups in euclidean space-time using the previous introduced
$U(1)$ groups. Finally we argue about the possible invariance of the fermionic
action with respect these new $SU(2)_{CS}$-like groups and its consequence on
the hadron temporal correlators.
