Is the CPT-norm always positive?

P,T,PT, and CPT invariance of Hermitian Hamiltonians

Currently, it has been claimed that certain Hermitian Hamiltonians have parity (P) and they are PT-invariant. We propose generalized definitions of time-reversal operator (T) and orthonormality such that all Hermitian Hamiltonians are P, T, PT, and CPT invariant. The PT-norm and CPT-norm are indefinite and definite respectively. The energy-eigenstates are either E-type (e.g., even) or O-type (e.g., odd). C mimics the charge-conjugation symmetry which is recently found to exist for a non-Hermitian Hamiltonian. For a Hermitian Hamiltonian it coincides with P.

C, PT, and CPT invariance of pseudo-Hermitian Hamiltonians

We propose construction of a unique and definite metric ($η_+$), time-reversal operator (T) and an inner product such that the pseudo-Hermitian matrix Hamiltonians are C, PT, and CPT invariant and PT(CPT)-norm is indefinite (definite). Here, P and C denote the generalized symmetries : parity and charge-conjugation respectively. The limitations of the other current approaches have been brought out.

Extension of the $CPT$ Theorem to non-Hermitian Hamiltonians and Unstable States

We extend the $CPT$ theorem to quantum field theories with non-Hermitian Hamiltonians and unstable states. Our derivation is a quite minimal one as it requires only the time independent evolution of scalar products, invariance under complex Lorentz transformations, and a non-standard but nonetheless perfectly legitimate interpretation of charge conjugation as an anti-linear operator. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its eigenvalues to either be real or to appear in complex conjugate pairs, forces the eigenvectors of such conjugat…

CPT Symmetry Without Hermiticity

In the literature the $CPT$ theorem has only been established for Hamiltonians that are Hermitian. Here we extend the $CPT$ theorem to quantum field theories with non-Hermitian Hamiltonians. Our derivation is a quite minimal one as it requires only the time independent evolution of scalar products and invariance under complex Lorentz transformations. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its eigenvalues to either be real or to appear in complex conjugate pairs, forces the eigenvectors of such conjugate pairs to be conjugates of each o…

量子信道张量积的极值性

On the Extremality of the Tensor Product of Quantum Channels

本文研究量子信道（CPT、UCP、UCPT映射）在张量积下极值性的保持，证明CPT和UCP映射保持极值性，而UCPT映射不一定保持。

Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics

In a recent paper it was shown that if a Hamiltonian H has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT. The inner product with respect to CPT is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator C for the non-Hermitian PT-symmetric Hamiltonian $H={1\over2}p^2+{1\over2}x^2 +iεx^3$ using perturbative techniques. It is also shown how to construct the operator C for $H={1\over2}p^2+{1\ov…