The paper by Bender, Brody, and Jones explores the extension of quantum mechanics beyond the standard formulation using Hermitian Hamiltonians. They introduce the concept of $\mathcal{PT}$ symmetry, where a Hamiltonian is not Hermitian but satisfies space-time reflection symmetry. This symmetry ensures that the spectrum of the Hamiltonian is real and positive. The authors identify a new symmetry, denoted $\mathcal{C}$, which is connected to the fact that there are equal numbers of positive-norm and negative-norm states in $\mathcal{PT}$-symmetric systems. This symmetry allows for the construction of a new inner product structure with positive definite norms, resolving the issue of indefinite metrics in $\mathcal{PT}$-symmetric theories. The $\mathcal{CPT}$ inner product is dynamically determined by the Hamiltonian and ensures that observables have real eigenvalues and the dynamics is unitary. The paper provides a general framework for extending quantum mechanics into the complex domain while maintaining physical consistency.The paper by Bender, Brody, and Jones explores the extension of quantum mechanics beyond the standard formulation using Hermitian Hamiltonians. They introduce the concept of $\mathcal{PT}$ symmetry, where a Hamiltonian is not Hermitian but satisfies space-time reflection symmetry. This symmetry ensures that the spectrum of the Hamiltonian is real and positive. The authors identify a new symmetry, denoted $\mathcal{C}$, which is connected to the fact that there are equal numbers of positive-norm and negative-norm states in $\mathcal{PT}$-symmetric systems. This symmetry allows for the construction of a new inner product structure with positive definite norms, resolving the issue of indefinite metrics in $\mathcal{PT}$-symmetric theories. The $\mathcal{CPT}$ inner product is dynamically determined by the Hamiltonian and ensures that observables have real eigenvalues and the dynamics is unitary. The paper provides a general framework for extending quantum mechanics into the complex domain while maintaining physical consistency.