Narrow Results

It is shown that the interacting Pais–Uhlenbeck (PU) oscillator necessarily leads to a description with a Hamiltonian that contains positive and negative energies associated with two oscillators. Descriptions with a positive definite Hamiltonians, considered by some authors, can hold only for a free PU oscillator. We demonstrate that the solutions of a self-interacting PU oscillator are stable on islands in the parameter space, as already observed in the literature. If we slightly modify the system, by considering a sine interaction term, and/or by taking unequal masses of the two oscillators, then the system is stable on the continents that extend from zero to infinity in the parameter space. Therefore, the PU oscillator is quite acceptable physical system.

We study a sixth-order derivative scalar field model in Minkowski spacetime as a toy model of higher-derivative critical gravity theories. This model is consistently quantized when using the Becchi–Rouet–Stora–Tyutin (BRST) quantization scheme even though it does not show gauge symmetry manifestly. Imposing a BRST quartet generated by two scalars and ghosts, there remains a nontrivial subspace with positive norm. This might be interpreted as a Minkowskian dual version of the unitary truncation in the logarithmic conformal field theory.

It is shown that in an axial-vector field theory the axial-vector field is always accompanied by a spin-0 field which has negative metric. Therefore, the theory has problem of negative probability and unitarity is broken. The same results are found in a theory of charged vector fields which are coupled to two fermions whose masses are different. These results are applied to the SM. It is found that both Z and W fields contain spin-0 component. Their masses are m_ϕ⁰ = m_te^28.4 = 3.78 × 10¹⁴ GeV and m_ϕ^± = m_te²⁷ = 9.31 × 10¹³ GeV respectively. A new perturbation theory of the SM is proposed. The propagators of Z and W fields in this new perturbation theory are derived in "unitary gauge." A minus sign is obtained in front of the scalar part of the propagators of W and Z fields. The minus sign indicates that the scalar fields have negative metric which leads to negative probability. Therefore, the unitarity of the SM is broken at about ~ 10¹⁴ GeV.

The Ward–Takahashi (WT) identities of the axial-vector currents and the charged vector currents of fermions are changed after spontaneous symmetry breaking. The spin-0 components of Z and W fields are revealed from the changed WT identities. The masses of these spin-0 components are at 10¹⁴ GeV. They are ghosts.

We present several solutions for the five-dimensional gravity models in the presence of bulk ghosts and tachyons to argue that these "troublesome" fields can be a useful model-building tool. The ghost-like signature of the kinetic term for a bulk scalar creates a minimum in the scale factor, removing the necessity for a negative tension brane in models with the compactified fifth dimension. It is shown that the model with the positive tension branes and a ghost field in the bulk leads to the radion stabilization. The bulk scalar with the variable sign kinetic term can be used to model both positive and negative tension branes of a finite width in the compact dimension. Finally, we present several ghost and tachyon field configurations in the bulk that lead to the localization of gravity in four dimensions, including one solution with the Gaussian profile for the metric, g_μν(y) = η_μνexp{-αy²}, which leads to a stronger localization of gravity than the Randall–Sundrum model.

A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually, this leads to collapse and loss of unitarity. In certain special cases, this does not happen, however, ghosts are benign.

We speculate that the Theory of Everything is a higher-derivative field theory, characterized by the presence of such benign ghosts and defined in a higher-dimensional bulk. Our Universe then represents a classical solution in this theory, having the form of a 3-brane embedded in the bulk.

The so-called bottleneck or ghost can appear after a saddle-node bifurcation, leaving a region in phase space by which the flow is attracted although no fixed points are present. Such ghosts, displayed by some dynamical systems, actually cause a delay of the flow. In this paper, we analyze a saddle-node ghost found in a biological model for the two-member hypercycle dynamics. The model predicts a scaling law of the dynamic delay caused by the ghost near the threshold: τ ~ ϕ^-1/2, consistent with previous results in physical systems. Possible biological meanings for such a dynamical phenomenon are outlined.

We review the occurrence of negative energies in Pais–Uhlenbeck oscillator. We point out that in the absence of interactions, negative energies are not problematic neither in the classical nor in the quantized theory. However, in the presence of interactions that couple positive and negative energy degrees of freedom, the system is unstable, unless the potential is bounded from below and above. We review some approaches in the literature that attempt to avoid the problem of negative energies in the Pais–Uhlenbeck oscillator.

It is shown that, anti-BRST symmetry is the quantized counterpart of local axial symmetry in gauge theories. An extended form of descent equations is worked out, which yields a set of modified consistent anomalies.