3 LA - UR - 93 - 4314 Space - Time Symmetries : P and CP Violation ¶

We begin with a few remarks on an explicit construction of a Bargmann-Wightman-Wigner-type quantum field theory [Phys. Lett. B 316, 102 (1993)] in which bosons and associated antibosons have opposite relative intrinsic parities. We then construct (1, 0) ⊕ (0, 1) Majorana (CP self conjugate) and Majorana-like (CΓ 5 self conjugate, Γ 5 = chirality operator) fields. We point out that this new structure in the space time symmetries may be relevant to P and CP violation. Until very recently, in all known quantum field theories, bosons and antibosons, composite or elementary, had the same relative intrinsic parity. However, about three decades ago [1], Bargmann, Wightman, and Wigner (BWW) had raised the possibility of a field theory in which a boson and its antiboson appear with opposite relative intrinsic parity. But, to the best of our knowledge, no explicit construction of a BWW-type quantum field theory existed. At this symposium, we presented an explicit construction of a quantum field theory in which a boson and its antiboson appear with opposite relative intrinsic parity; and we thus provided the first example in (3, 1)-space-time of a quantum field theory of the BWW-type. Since the explicit construction of this theory has been just published [2], it is not necessary to repeat the complete construction here; instead, we take the liberty of making a few remarks on such a theory. These remarks are followed by further investigation of the P and CP structure of the (1, 0) ⊕ (0, 1) representation space.