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We give a simple discussion of ghosts, unitarity violation, negative norm states and quantum vs classical behavior in the simplest model with four derivative action - the Pais-Uhlenbeck oscillator. We also point out that the normalizable vacuum state (in the sense defined below) of this model can be understood as spontaneous breaking of the emergent conformal symmetry. We provide an example of an interacting system that couples the particle and ghost degrees of freedom and nevertheless remains unitary on both classical and quantum level.
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We study higher derivative terms associated with scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired by the Pais-Uhlenbeck oscillator, given by $alphapartial_{mu}partial^{mu}phipartial_{ u}partial^{ u}phi.$ We investigate the cosmological dynamics in a phase space. For $alpha>0$, we provide conditions for the stability of de Sitter solutions. In this case the crossing of the phantom divide $w_{DE}=-1$ occurs once; thereafter, the equation of state parameter remains under this line, asymptotically reaching towards the de Sitter solution from below. For $alpha<0,$ which is the portion of the parameter space where in addition to crossing the phantom divide, cyclic behavior is possible, we present regions in the parameter space where, according to Smilgas classification the ghost has benign or malicious behavior.
We present a new understanding of the unstable ghost-like resonance which appears in theories such as quadratic gravity and Lee-Wick type theories. Quantum corrections make this resonance unstable, such that it does not appear in the asymptotic spectrum. We prove that these theories are unitary to all orders. Unitarity is satisfied by the inclusion of only cuts from stable states in the unitarity sum. This removes the need to consider this as a ghost state in the unitarity sum. However, we often use a narrow-width approximation where we do include cuts through unstable states, and ignore cuts through the stable decay products. If we do this with the unstable ghost resonance at one loop, we get the correct answer only by using a contour which was originally defined by Lee and Wick. The quantum effects also provide damping in both the Feynman and the retarded propagators, leading to stability under perturbations.
A recent paper by the CDF collaboration suggests (but does not claim) an anomalous event sample containing muons produced with large impact parameter, often with high multiplicity and at small angles from one another. This curious hint of a signal is potentially consistent with the hidden valley scenario, as well as with some other classes of models. Despite its tenuous nature, this hint highlights the experimental difficulties raised by such signals, and merits some consideration. Some of the simplest interpretations of the data, such as a light neutral particle decaying to muon and/or tau pairs, are largely disfavored; three-body decays to $tautau u$ appear slightly better. An alternative speculative possibility -- a micro-cascade decay -- might be consistent with the data. It is suggested that the experimentalists involved provide additional plots showing invariant mass distributions of same- and opposite-sign dimuon pairs, invariant masses of various classes of displaced vertices, and spatial correlations among vertices within a cone.
We look at simple BPS systems involving more than one field. We discuss the conditions that have to be imposed on various terms in Lagrangians involving many fields to produce BPS systems and then look in more detail at the simplest of such cases. We analyse in detail BPS systems involving 2 interacting Sine-Gordon like fields, both when one of them has a kink solution and the second one either a kink or an antikink solution. We take their solitonic static solutions and use them as initial conditions for their evolution in Lorentz covaria
We discuss aspects of non-perturbative unitarity in quantum field theory. The additional ghost degrees of freedom arising in truncations of an effective action at a finite order in derivatives could be fictitious degrees of freedom. Their contributions to the fully-dressed propagator -- the residues of the corresponding ghost-like poles -- vanish once all operators compatible with the symmetry of the theory are included in the effective action. These fake ghosts do not indicate a violation of unitarity.
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