In this talk I will review non-Hermitian PT-symmetric quantum mechanics and quantum field theory. To define a proper quantum theory with unitary time evolution and positive-definite norm, it is necessary to introduce a new symmetry operator called C. The calculation of the C operator is the central task to construct PT-symmetric quantum field theory. I will use PT-symmetric i\phi^3 as an example to demonstrate this calculation. As an application, I will then re-investigate the Lee model using this new idea. I will show that with this PT-symmetric interpretation, the ghost state that has haunted the Lee model for 50 years does not exist. I will also show that the quantum-field-theoretic C operator is actually a generalization of the intrinsic parity operator.
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