Finite Theory of Quantum Electrodynamics

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

doi:10.1103/physrevd.2.1033

Cited by 436 publications

(365 citation statements)

References 34 publications

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“…As shown in Ref. [2], an inner product defined with respect to PT -conjugation leads to an indefinite metric of the type investigated earlier by Lee and Wick [7]. However, an inner product defined with respect to CPTconjugation leads to a positive definite metric, and hence positive probabilities [2,8].…”

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confidence: 96%

Semiclassical analysis of a complex quartic Hamiltonian

2006

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It is necessary to calculate the C operator for the non-Hermitian PT -symmetric Hamiltonian H = 1 2 p 2 + 1 2 µ 2 x 2 − λx 4 in order to demonstrate that H defines a consistent unitary theory of quantum mechanics. However, the C operator cannot be obtained by using perturbative methods. Including a small imaginary cubic term gives the Hamiltonian H = 1 2 p 2 + 1 2 µ 2 x 2 + igx 3 − λx 4 , whose C operator can be obtained perturbatively. In the semiclassical limit all terms in the perturbation series can be calculated in closed form and the perturbation series can be summed exactly. The result is a closed-form expression for C having a nontrivial dependence on the dynamical variables x and p and on the parameter λ.

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confidence: 96%

Semiclassical analysis of a complex quartic Hamiltonian

2006

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“…Lee and Wick [279,280] proposed, in the late sixties, a finite version of QED; based upon this proposition, Grinstein et al constructed a modification to the standard model known as the Lee-Wick Standard Model [281]; this model aspires to provide an alternative to supersymmetry. A feature of these models is the presence of phantom fields [282].…”

Section: Lee-wick and Quintommentioning

confidence: 99%

A critical review of classical bouncing cosmologies

2015

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Given the proliferation of bouncing models in recent years, we gather and critically assess these proposals in a comprehensive review. The PLANCK data shows an unmistakably red, quasi scaleinvariant, purely adiabatic primordial power spectrum and no primary non-Gaussianities. While these observations are consistent with inflationary predictions, bouncing cosmologies aspire to provide an alternative framework to explain them. Such models face many problems, both of the purely theoretical kind, such as the necessity of violating the NEC and instabilities, and at the cosmological application level, as exemplified by the possible presence of shear. We provide a pedagogical introduction to these problems and also assess the fitness of different proposals with respect to the data. For example, many models predict a slightly blue spectrum and must be fine-tuned to generate a red spectral index; as a side effect, large non-Gaussianities often result.We highlight several promising attempts to violate the NEC without introducing dangerous instabilities at the classical and/or quantum level. If primordial gravitational waves are observed, certain bouncing cosmologies, such as the cyclic scenario, are in trouble, while others remain valid. We conclude that, while most bouncing cosmologies are far from providing an alternative to the inflationary paradigm, a handful of interesting proposals have surfaced, which warrant further research. The constraints and lessons learned as laid out in this review might guide future research.

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“…Theories that are not causal appear, at first glance, to be fraught with paradoxical behavior that renders them inconsistent. In the late 1960's Lee and Wick [1], [2] proposed an extension of quantum electrodynamics where the Pauli-Villars regulator is treated as a finite mass scale. In this theory the Fourier transform of the gauge field two-point function has massive "Lee-Wick photon" poles with wrong sign residues.…”

Section: Introductionmentioning

confidence: 99%

Causality as an emergent macroscopic phenomenon: The Lee-WickO(N)model

2009

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In quantum mechanics the deterministic property of classical physics is an emergent phenomenon appropriate only on macroscopic scales. Lee and Wick introduced Lorentz invariant quantum theories where causality is an emergent phenomenon appropriate for macroscopic time scales. In this paper we analyze a Lee-Wick version of the O(N ) model. We argue that in the large N limit this theory has a unitary and Lorentz invariant S matrix and is therefore free of paradoxes in scattering experiments. We discuss some of its acausal properties.

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Finite Theory of Quantum Electrodynamics

Cited by 436 publications

References 34 publications

Semiclassical analysis of a complex quartic Hamiltonian

Semiclassical analysis of a complex quartic Hamiltonian

A critical review of classical bouncing cosmologies

Causality as an emergent macroscopic phenomenon: The Lee-WickO(N)model

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