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We suggest and briefly review a new sort of superrenormalizable models of higher derivative quantum gravity. The higher derivative terms in the action can be introduced in such a way that all the unphysical massive states have complex…
We use the ideas of symplectic quantization for quantizing fields in finite volumes. We consider, as examples, the Klein-Gordon and electromagnetic fields in three dif- ferent boxes. As a second idea we consider the given boundary…
Scattering transform is a well known powerful tool for quantisation of field theories in (1+1) dimensions. Conventionally only those models whose classical counterparts admit a Lax pair (origin of which is always mysterious) have been…
..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational…
General relativity has its successes at the local astrophysical level, however, it seems to be insufficient in describing the Universe at large scales. In this work we investigate how the most general field theories in the context of…
The effective field theory of massive gravity had long been formulated in a generally covariant way arXiv:hep-th/0210184. Using this formalism, it has been found recently that there exists a class of massive nonlinear theories that are free…
We constrain effective field theories by going beyond the familiar positivity bounds that follow from unitarity, analyticity, and crossing symmetry of the scattering amplitudes. As interesting examples, we discuss the implications of the…
We investigate the details of the canonical quantization of effective quantum field theories in anti-de Sitter spacetime, emphasizing the stability of the quantum vacuum. We take the scalar and Maxwell fields as examples. For the…
A cosmology inspired structure for phase space is introduced, which leads to finitization and lattice-like discretization of position and momentum eigenvalues in a preferred, cosmic frame. Lorentz invariance is broken at very high energies,…
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…
In this work we develop a theoretical framework for Gauss-Bonnet modified gravity theories, in which ghost modes can be eliminated at the equations of motion level. Particularly, after we present how the ghosts can occur at the level of…
The origin of the observed dark energy could be explained entirely within the standard model, with no new fields required. We show how the low-energy sector of the chiral QCD Lagrangian, once embedded in a non-trivial spacetime, gives rise…
We study an extension of the symplectic formalism in order to quantize reducible systems. We show that a procedure like {\it ghost-of-ghost} of the BFV method can be applied in terms of Lagrange multipliers. We use the developed formalism…
We investigate the non-perturbative quantization of phantom and ghost degrees of freedom by relating their representations in definite and indefinite inner product spaces. For a large class of potentials, we argue that the same physical…
We develop a Lagrangian quantization formalism for a class of theories obtained by the restriction of the configuration space of gauge fields from a wider (parental) gauge theory. This formalism is based on application of the…
A nonlocal generalization of quantum field theory in which momentum space is the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed. Functional integrals in this theory are proved to exist. Renormalized quantum field model…
The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime…
According to the holographic bound, there is only a finite density of degrees of freedom in space when gravity is taken into account. Conventional quantum field theory does not conform to this bound, since in this framework, infinitely many…
In this work we shall address the ghost issue of $F\left( R,\mathcal{G} \right)$ gravity, which is known to be plagued with ghost degrees of freedom. These ghosts occur due to the presence of higher than two derivatives in the field…
Theories which contain ghost fields are considered to be invalid. It is assumed that for such theories the energy is unbounded from below, and the theory will be unstable, allowing the creation of particle pairs with arbitrarily large…