We revisit the previously unsolved problems of ensuring Lorentz invariance and non-perturbative unitarity in Lee-Wick theories. We base our discussion on an ultraviolet completion of QED by Lee-Wick ghost fields, which is argued to be asymptotically safe. We argue that as long as the state space is based upon a suitable choice of distributions of a type invented by Gel'fand and Shilov, the Lee-Wick ghosts can be eliminated while preserving Lorentz invariance to produce a unitary theory. The method for eliminating ghosts is in principle non-perturbatively well-defined, in contrast with some previous proposals. We also point out a second, independent mechanism for producing a unitary theory, based on a covariant constraint on the maximum four-momentum, which would imply an amusing connection, based on naturalness, between the coupling constant and the hierarchy of scales in the theory. We further emphasize that the resulting theory is causal, and point out some analogies between between the behaviour of Lee-Wick ghost degrees of freedom and black holes.
Most discussions of propagators in Lee-Wick theories focus on the presence of two massive complex conjugate poles in the propagator. We show that there is in fact only one pole near the physical region, or in another representation three pole-like structures with compensating extra poles. The latter modified Lehmann representation is useful caculationally and conceptually only if one includes the resonance structure in the spectral integral.
On the basis of the canonical quantization procedure, in which we need the indefinite metric Hilbert space, we formulate field diagonal representation for the scalar Lee-Wick model. Euclidean path integral for the model is then constructed in terms of the eigenvector of field operators. Taking the quantum mechanical Lee-Wick model as an example, we demonstrate how to formulate path integrals for such systems in detail. We show that, despite the use of indefinite metric representation, integration contours for ghost degrees can be taken along the real axis.
Lee-Wick-like scalar model near a Dirichlet plate is considered in this work. The modified propagator for the scalar field due to the presence of a Dirichlet boundary is computed, and the interaction between the plate and a point-like scalar charge is analysed. The non-validity of the image method is investigated and the results are compared with the corresponding ones obtained for the Lee-Wick gauge field and for the standard Klein-Gordon field.
In this letter we study some aspects of the planar Lee-Wick electrodynamics near a perfectly conducting line (unidimensional mirror). Specifically, the modified Lee-wick propagator due to the presence of a conducting line is calculated, and the interaction between the mirror and the point-like charge is investigated. It is shown that the behavior of this interaction is very different from the one already known for the $(3+1)$-dimensional Lee-Wick electrodynamics, where we have a planar mirror. It is also shown that the image method is not valid in planar Lee-Wick electrodynamics and the dimens…
We reconsider the Lee-Wick (LW) models and compare their properties to the properties of the models that contain purely virtual particles. We argue against the LW premise that unstable particles can be removed from the sets of incoming and outgoing states in scattering processes. The removal leads to a non-Hermitian classical limit, besides clashing with the observation of the muon. If, on the other hand, all the states are included, the LW models have a Hamiltonian unbounded from below or negative norms. Purely virtual particles, on the contrary, lead to a Hermitian classical limit and are ab…
In the seventies, Lee and Wick proposed an interesting modification of classical electrodynamics that renders it finite at the quantum level. At the classical level, this modified theory leads to a regular linear potential at short distances while also reproducing the Coulomb potential at large distances. It is shown that a suitable modification of the Lee-Wick idea can also lead to a linear potential at large distances. For this purpose, we study an Abelian model that ``simulates" the QCD confining phase while maintaining the Coulomb behavior at short distances. This paper is organized in thr…
We construct a theory of real scalar fields that interpolates between two different theories: a Lee-Wick theory with $N$ propagator poles, including $N-1$ Lee-Wick partners, and a nonlocal infinite-derivative theory with kinetic terms modified by an entire function of derivatives with only one propagator pole. Since the latter description arises when taking the $N\rightarrow\infty$ limit, we refer to the theory as "asymptotically nonlocal." Introducing an auxiliary-field formulation of the theory allows one to recover either the higher-derivative form (for any $N$) or the Lee-Wick form of the …
The "fakeon" is a fake degree of freedom, i.e. a degree of freedom that does not belong to the physical spectrum, but propagates inside the Feynman diagrams. Fakeons can be used to make higher-derivative theories unitary. Moreover, they help us clarify how the Lee-Wick models work. In this paper we study the fakeon models, that is to say the theories that contain fake and physical degrees of freedom. We formulate them by (nonanalytically) Wick rotating their Euclidean versions. We investigate the properties of arbitrary Feynman diagrams and, among other things, prove that the fakeon models are…
We derive a singular solution for the rotating counterpart of Lee-Wick gravity having a point source in a higher-derivative theory. We critically analyze the thermodynamics of such a thermal system by evaluating mass parameters, angular velocity, and Hawking temperature. The system follows the first law of thermodynamics and leads to the expression of entropy. We further discuss the stability and phase transition of the theory by evaluating heat capacity and free energy. The phase transition occurs at the point of divergence and the temperature is maximum. Remarkably, the black hole is unstabl…
Asymptotically nonlocal field theories represent a sequence of higher-derivative theories whose limit point is a ghost-free, infinite-derivative theory. Here, we extend previous work on pure scalar and Abelian gauge theories to asymptotically nonlocal non-Abelian theories. In particular, we confirm that there is a limit in which the Lee-Wick spectrum can be decoupled, but where the hierarchy problem is resolved via an emergent nonlocal scale that regulates loop diagrams and that is hierarchically smaller than the lightest Lee-Wick resonance.
We study perturbative unitarity in the scalar sector of the Myers-Pospelov model. The model introduces a preferred four-vector $n$ which breaks Lorentz symmetry and couples to a five-dimension operator. When the preferred four-vector is chosen in the pure timelike or lightlike direction, the model becomes a higher time derivative theory, leading to a cubic dispersion relation. Two of the poles are shown to be perturbatively connected to the standard ones, while a third pole, which we call the Lee-Wick-like pole, is associated to a negative metric, in Hilbert space, threatening the preservation…
Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces
Universidade Federal de Juiz de Fora（茹伊斯德福拉联邦大学）；Universidade Federal Rural do Rio de Janeiro（里约热内卢联邦农村大学）；Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）
We canonically quantize $(2+1)$-dimensional electrodynamics including a higher-derivative Chern-Simons term. The effective theory describes a standard photon and an additional degree of freedom associated with a massive ghost. We find the Hamiltonian and the algebra satisfied by the field operators. The theory is characterized by an indefinite metric in the Hilbert space that brings up questions on causality and unitarity. We study both of the latter fundamental properties and show that microcausality as well as perturbative unitarity up to one-loop order are conserved when the Lee-Wick prescr…
