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• W2156896064 abstract "In a recent paper Jones and Mateo used operator techniques to show that the non-Hermitian $mathcal{P}mathcal{T}$-symmetric wrong-sign quartic Hamiltonian $H=frac{1}{2}{p}^{2}ensuremath{-}g{x}^{4}$ has the same spectrum as the conventional Hermitian Hamiltonian $stackrel{texttildelow{}}{H}=frac{1}{2}{p}^{2}+4g{x}^{4}ensuremath{-}sqrt{2g}x$. Here, this equivalence is demonstrated very simply by means of differential-equation techniques and, more importantly, by means of functional-integration techniques. It is shown that the linear term in the Hermitian Hamiltonian is anomalous; that is, this linear term has no classical analog. The anomaly arises because of the broken parity symmetry of the original non-Hermitian $mathcal{P}mathcal{T}$-symmetric Hamiltonian. This anomaly in the Hermitian form of a $mathcal{P}mathcal{T}$-symmetric quartic Hamiltonian is unchanged if a harmonic term is introduced into $H$. When there is a harmonic term, an immediate physical consequence of the anomaly is the appearance of bound states; if there were no anomaly term, there would be no bound states. Possible extensions of this work to $ensuremath{-}{ensuremath{phi}}^{4}$ quantum field theory in higher-dimensional space-time are discussed." @default.
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• W2156896064 date "2006-07-24" @default.
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• W2156896064 title "Equivalence of a complex<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi mathvariant=script>P</mml:mi><mml:mi mathvariant=script>T</mml:mi></mml:math>-symmetric quartic Hamiltonian and a Hermitian quartic Hamiltonian with an anomaly" @default.
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• W2156896064 doi "https://doi.org/10.1103/physrevd.74.025016" @default.
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