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arXiv · hep-th/0508105

Dual PT-Symmetric Quantum Field Theories

Carl M. Bender·H. F. Jones·R. J. Rivers
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Abstract

Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a $γ_5$ mass term the Hamiltonian is $\cal PT$-symmetric. Depending on the mass parameter this symmetry may be either broken or unbroken. When the $\cal PT$ symmetry is unbroken, the spectrum of the quantum field theory is real. For the $\cal PT$-symmetric version of the massive Thirring model in two-dimensional space-time, which is dual to the $\cal PT$-symmetric scalar Sine-Gordon model, an exact construction of the $\cal C$ operator is given. It is shown that the $\cal PT$-symmetric massive Thirring and Sine-Gordon models are equivalent to the conventional Hermitian massive Thirring and Sine-Gordon models with appropriately shifted masses.

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Carl M. Bender, H. F. Jones, R. J. Rivers. 2005-08-15. Dual PT-Symmetric Quantum Field Theories. https://doi.org/10.1016/j.physletb.2005.08.087

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