Unitarity in the Nθθ sector of soluble model with indefinite metric

Lee, T.D.; Wick, G. C.

doi:10.1016/0550-3213(69)90275-2

Cited by 82 publications

(22 citation statements)

References 8 publications

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“…Our propagator (19) reproduces this expression (20). It can be seen after the calculation of the tree level Feynman diagram describing an exchange of two point-like particles with a graviton.…”

Section: Resultssupporting

confidence: 53%

Renormalizable and Unitary Model of Quantum Gravity

Larin

2019

Symmetry

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We consider R + R 2 relativistic quantum gravity with the action where all possible terms quadratic in the curvature tensor are added to the Einstein-Hilbert term. This model was shown to be renormalizable in the work by K.S. Stelle. In this paper, we demonstrate that the R + R 2 model is also unitary contrary to the statements made in the literature, in particular in the work by Stelle. New expressions for the R + R 2 Lagrangian within dimensional regularization and the graviton propagator are derived. We demonstrate that the R + R 2 model is a good candidate for the fundamental quantum theory of gravity.

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Section: Resultssupporting

confidence: 53%

Renormalizable and Unitary Model of Quantum Gravity

Larin

2019

Symmetry

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“…(Since C obeys [C, H ] = 0, C 2 = 1, energy eigenstates are eigenstates of C with eigenvalue ±1, to thus take care of the minus sign in (63).) Now while we have seen that we do not need to formulate the fourth-order propagator theory of (61) in a Krein space, we note that if one does, then one can still obtain unitarity by the Lee-Wick mechanism [20][21][22]. Specifically, one adds interactions that cause the poles in the propagator to move into the complex energy plane so that the associated states then become unstable and do not appear as asymptotic in or out states.…”

Section: Ghost Problem Of Second-plus Fourth-order Theoriesmentioning

confidence: 95%

“…In consequence of this anomaly, there is no pole in the fermion anti-fermion scattering amplitude even though the mass non-trivially obeys a selfconsistent gap type equation. 21 In a conformal gravity theory that is realized with anomalous dimensions, one might expect an analog of the Baker-Johnson evasion to occur.…”

Section: Conclusion and Commentsmentioning

confidence: 98%

“…Thus for T μν MF = (ρ MF + p MF )U μ U ν + p MF g μν − MF g μν , the trace condition 3 p MF − ρ MF − 4 MF = 0 allows us to write T μν MF = (ρ MF + p MF )[U μ U ν + g μν /4], with its MF -independent finite part being minimized in (81). 21 If there is a dynamical Goldstone pole in the fermion anti-fermion scattering amplitude, its residue will obey a self-consistent equation. However, in and of itself, the fact that there might be a non-trivial solution to this self-consistent equation does not mean that there necessarily is a massless pole.…”

Section: Conclusion and Commentsmentioning

confidence: 99%

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Comprehensive solution to the cosmological constant, zero-point energy, and quantum gravity problems

Mannheim

2010

Gen Relativ Gravit

133

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We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. In our approach quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.

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“…Firstly, in Lee model, the renormalizations of the V -fermion mass m V and coupling constant g should be taken into account, and the Hamiltonian (6) is non-Hermitian. Thus we should investigate the unitarity of the S-matrix carefully 31,32 . Secondly, the Hilbert space of heavy fermion is spanned by four basis states, i.e., |0 , ψ †…”

Section: Relation To Lee Modelmentioning

confidence: 99%

Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays

2009

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We present a quantum field theoretical approach based on the Lehmann-Symanzik-Zimmermann reduction for the multi-photon scattering process in a nano-architecture consisting of the coupledresonator arrays (CRA), which are also coupled to some artificial atoms as a controlling quantum node. By making use of this approach, we find the bound states of single photon for an elementary unit, the T-type CRA, and explicitly obtain its multi-photon scattering S-matrix in various situations. We also use this method to calculate the multi-photon S-matrices for the more complex quantum network constructed with main T-type CRA's, such as a H-type CRA waveguide.

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Unitarity in the Nθθ sector of soluble model with indefinite metric

Cited by 82 publications

References 8 publications

Renormalizable and Unitary Model of Quantum Gravity

Renormalizable and Unitary Model of Quantum Gravity

Comprehensive solution to the cosmological constant, zero-point energy, and quantum gravity problems

Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays

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