Related papers: On the Quantisation of Complex Higher Derivative T…
Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the…
If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which…
We analyze the unitarity properties of higher derivative quantum field theories which are free of ghosts and ultraviolet singularities. We point out that in spite of the absence of ghosts most of these theories are not unitary. This result…
The Pais-Uhlenbeck model is a quantum theory described by a higher-derivative field equation. It has been believed for many years that this model possesses ghost states (quantum states of negative norm) and therefore that this model is a…
In this work, we investigate higher-derivative quantum field theories and the problem of Ostrogradsky instability within an open-system Keldysh-Lindblad framework. Coupling the ghost sector to dissipative baths generates non-perturbative…
We quantise integrable point-particle systems with opposite-sign kinetic terms and nontrivial interactions. Using methods from separability theory, we show that previously determined classical stability conditions also imply discrete…
An alternative to the effective field theory approach to treat ghosts in higher derivative theories is to attempt to integrate them out via the Euclidean path integral formalism. It has been suggested that this method could provide a…
We discuss exactly solvable systems involving integrals of motion with higher powers of momenta. If one of these integrals is chosen for the Hamiltonian, we obtain a higher-derivative system involving ghosts, i.e. a system whose Hamiltonian…
Higher derivative scalar interactions can give rise to interesting cosmological scenarios. We present a complete classification of such operators that can yield sizeable effects without introducing ghosts and, at the same time, define an…
We address the long-standing ``ghost problem" in higher time-derivative theories (HTDTs), where quantisation typically yields sectors with either unbounded spectra or non-normalisable eigenstates; both rendering the theory unphysical. We…
Perturbation theory for gravity in dimensions greater than two requires higher derivatives in the free action. Higher derivatives seem to lead to ghosts, states with negative norm. We consider a fourth order scalar field theory and show…
The inclusion of higher derivatives is a necessary condition for a renormalizable or superrenormalizable local theory of quantum gravity. On the other hand, higher derivatives lead to classical instabilities and a loss of unitarity at the…
The aim of these notes is to provide a self-contained review of why it is generically a problem when a solution of a theory possesses ghost fields among the perturbation modes. We define what a ghost field is and we show that its presence…
We present a simple class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e. with a ghost. We prove analytically that the classical motion of the system is completely…
The Ostrogradski ghost problem that appears in higher derivative theories containing constraints has been considered here. Specifically we have considered systems where only the second class constraints appear. For these kind of systems, it…
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate…
We review the formulation of quantum field theories with purely virtual particles, a new type of degrees of freedom that can mediate interactions without ever appear as external on-shell states. This property allows to solve the problem of…
The role of higher derivative operators in 4D effective field theories is discussed in both non-supersymmetric and supersymmetric contexts. The approach, formulated in the Minkowski space-time, shows that theories with higher derivative…
We study the renormalization group flow of gravity coupled to scalar matter using functional renormalization group techniques. The novel feature is the inclusion of higher-derivative terms in the scalar propagator. Such terms give rise to…
Ghosts have been a stumbling block in the development of a UV complete quantum field theory for gravity. We discuss how difficulties associated with ghosts are overcome in the context of 0+1d QFT. Obtaining a probability interpretation is…