On the Time Reversal in the Quantized Field Theory

Abstract

The possibility of time reversal transformation is investigated from the general viewpoint of the quantized field theory. The time reversal transformation is so defined as to preserve the canonical formalism of the theory. It is found in §2 that there are two kinds of such transformations, which are shown to correspond to the so-called Pauli’s and Wigner’s transformations, respectively. In §3 the transformation properties of physical quantities under these transformations are examined and then the physical meanings of time reversal are clarified. In §4 some considerations are made as to whether the invariance requirement under the time reversal really imposes restrictions on the form of interaction Hamiltonian and the otherwise undermined phase factors of the coupling constants of the Fermi and Yang-Tiomno interactions. Finally the connection between the generalized time reversal transformation and the concept of the family of elementary particles is studied. In the appendix the transformation is further applied to the Pais’ theory of baryon-meson-photon system.