Department of Mathematics2024-11-0920060217-751X10.1142/S0217751X060288132-s2.0-33744502871http://dx.doi.org/10.1142/S0217751X06028813https://hdl.handle.net/20.500.14288/7381Generalized parity (P), time-reversal (T), and charge-conjugation (C) operators were initially defined in the study of the pseudo-Hermitian Hamiltonians. We construct a concrete realization of these operators for Klein-Gordon fields and show that in this realization PT and C operators respectively correspond to the ordinary time-reversal and charge-grading operations. Furthermore, we present a complete description of the quantum mechanics of Klein-Gordon fields that is based on the construction of a Hilbert space with a relativistically invariant, positive-definite, and conserved inner product. In particular we offer a natural construction of a position operator and the corresponding localized and coherent states. The restriction of this position operator to the positive-frequency fields coincides with the Newton-Wigner operator. Our approach does not rely on the conventional restriction to positive-frequency fields. Yet it provides a consistent quantum mechanical description of Klein-Gordon fields with a genuine probabilistic interpretation.PhysicsNuclear physicsParticles and fields physicsJournal Article1793-656X2385842000075512