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PCT, a fundamental symmetry of particle physics, is derived assuming Lorentz invariance and positivity of the spectrum of the Hamiltonian. What happens if we assume only Lorentz invariance and PCT symmetry? Hamiltonians having this property need not be Hermitian but, except when PCT is spontaneously broken, the energy levels of such Hamiltonians are all real and positive!
In this talk I examine some elementary quantum systems whose Hamiltonians are non-Hermitian but PCT-symmetric. These systems have weird and remarkable properties, and the classical theories underlying these quantum systems also have strange and interesting behaviors. Examples of such Hamiltonians are H=p2+ix3 and H=p2-x4. Hamiltonians such as these may be regarded as complex deformations of conventional Hermitian Hamiltonians. Thus, in this talk I will be studying the analytic continuation of conventional classical mechanics and quantum mechanics into the complex plane.
I will also examine the corresponding non-Hermitian quantum field theories. Field theories whose self-interaction terms are igφ3 and -gφ4 have strange and interesting properties and may have possible experimental applications in such areas as band theory and in Higgs particle physics.
