The complex pendulum

摘要

This talk proposes a generalization of conventional quantum mechanics. In conventional quantum mechanics one imposes the condition H-dagger = H, where dagger represents complex conjugation and matrix transpose, to ensure that the Hamiltonian has a real spectrum. By replacing this mathematical condition with the weaker and more physical requirement H double dagger = H, where double dagger = PT represents combined parity reflection and time reversal, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These PT-symmetric theories may be viewed as analytic continuations of conventional theories from real to complex-phase space. This talk describes the unusual classical and quantum properties of PT-symmetric quantum-mechanical and quantum-field-theoretic models. (C) 1999 Elsevier Science B.V. All rights reserved. [References: 13]