Scalar Quantum Field Theory with Cubic Interaction

Abstract

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 construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.

Corrected expressions in equations (20) and (21)

References in corpus (9)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• Must a Hamiltonian be Hermitian?
• Quantum Entanglement of Moving Bodies
• Supersymmetry and the spontaneous breakdown of PT symmetry
• Solution of Schwinger-Dyson Equations for $\mathcal{P}\mathcal{T}$-Symmetric Quantum Field Theory
• Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics
• The C Operator in PT-Symmetric Quantum Theories

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