  We begin with a few remarks on an explicit construction of a
Bargmann-Wightman-Wigner-type quantum field theory [Phys. Lett. B {\bf 316},
102 (1993)] in which bosons and associated antibosons have opposite relative
intrinsic parities. We then construct $(1,0)\oplus(0,1)$ Majorana ($CP$ self
conjugate) and Majorana-like ($C\Gamma^5$ self conjugate, $\Gamma^5=$ chirality
operator) fields. We point out that this new structure in the space time
symmetries may be relevant to $P$ and $CP$ violation.
