Comment on ``New ansatz for metric operator calculation in pseudo-Hermitian field theory'' (2009)
Bender, Carl M., Benincasa, Gregorio, Jones, Hugh F.
In a recent Brief Report by Shalaby a new first-order perturbative calculation of the metric operator for an $i\phi^3$ scalar field theory is given. It is claimed that the result is an improvement on...
Bender, Carl M., Besseghir, Karim, Jones, Hugh F., Yin, Xinghui
The energy eigenvalues of the class of non-Hermitian PT-symmetric Hamiltonians $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) are real, positive, and discrete. The behavior of these eigenvalues has been...
Interactions of Hermitian and non-Hermitian Hamiltonians (2007)
Bender, Carl M., Jones, Hugh F.
The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian Hamiltonians, each of which individually has a real energy spectrum, is explored by means of a number of soluble models....
Faster than Hermitian Quantum Mechanics (2006)
Bender, Carl M., Brody, Dorje C., Jones, Hugh F., Meister, Bernhard K.
Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into |psi_F>. Consider the following quantum...
Bender, Carl M., Brody, Dorje C., Chen, Jun-Hua, Jones, Hugh F., Milton, Kimball A., Ogilvie, Michael C.
In a recent paper Jones and Mateo used operator techniques to show that the non-Hermitian $\cP\cT$-symmetric wrong-sign quartic Hamiltonian $H=\half p^2-gx^4$ has the same spectrum as the...
Semiclassical analysis of a complex quartic Hamiltonian (2005)
Bender, Carl M., Brody, Dorje C., Jones, Hugh F.
It is necessary to calculate the C operator for the non-Hermitian PT-symmetric Hamiltonian H=\half p^2+\half\mu^2x^2-\lambda x^4 in order to demonstrate that H defines a consistent unitary theory of...
Semiclassical Calculation of the C Operator in PT-Symmetric Quantum Mechanics (2004)
Bender, Carl M., Jones, Hugh F.
To determine the Hilbert space and inner product for a quantum theory defined by a non-Hermitian $\mathcal{PT}$-symmetric Hamiltonian $H$, it is necessary to construct a new time-independent...
Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction (2004)
Bender, Carl M., Brody, Dorje C., Jones, Hugh F.
It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics...
Scalar Quantum Field Theory with Cubic Interaction (2004)
Bender, Carl M., Brody, Dorje C., Jones, Hugh F.
In this paper it is shown that an i phi^3 field theory is a physically acceptable field theory model (the spectrum is positive and the theory is unitary). The demonstration rests on the perturbative...
Must a Hamiltonian be Hermitian? (2003)
Bender, Carl M., Brody, Dorje C., Jones, Hugh F.
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT...
Complex Extension of Quantum Mechanics (2002)
Bender, Carl M., Brody, Dorje C., Jones, Hugh F.
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex...