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We analyze the R + R2 model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a self-consistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters., Comment: 12 pages

We consider the unitary Abelian Higgs model and investigate its spectral functions at one-loop order. This analysis allows to disentangle what is physical and what is not at the level of the elementary particle propagators, in conjunction with the Nielsen identities. We highlight the role of the tadpole graphs and the gauge choices to get sensible results. We also introduce an Abelian Curci-Ferrari action coupled to a scalar field to model a massive photon which, like the non-Abelian Curci-Ferarri model, is left invariant by a modified non-nilpotent BRST symmetry. We clearly illustrate its non-unitary nature directly from the spectral function viewpoint. This provides a functional analogue of the Ojima observation in the canonical formalism: there are ghost states with nonzero norm in the BRST-invariant states of the Curci-Ferrari model., 32 pages, 12 figures

We consider R + R 2 relativistic quantum gravity with the action where all possible terms quadratic in the curvature tensor are added to the Einstein-Hilbert term. This model was shown to be renormalizable in the work by K.S. Stelle. In this paper, we demonstrate that the R + R 2 model is also unitary contrary to the statements made in the literature, in particular in the work by Stelle. New expressions for the R + R 2 Lagrangian within dimensional regularization and the graviton propagator are derived. We demonstrate that the R + R 2 model is a good candidate for the fundamental quantum theory of gravity.

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. Such fields can exist as part of a hidden matter in the Universe if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT- invariance. Restrictions on mass-spectrum of CPT-violating fields are found. Local fields that annihilate vacuum state and violate CPT- invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particulary needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed., Comment: Latex 23 pages, sent to "Foundations of Physics"

In previous work done by us and coworkers, we have been able to construct a local, non-Abelian gauge invariant action with a mass parameter, based on the nonlocal gauge invariant mass dimension two operator F1/D^2F. The renormalizability of the resulting action was proven to all orders of perturbation theory, in the class of linear covariant gauges. We also discussed the perturbative equivalence of the model with ordinary massless Yang-Mills gauge theories when the mass is identically zero. Furthermore, we pointed out the existence of a BRST symmetry with corresponding nilpotent charge. In this paper, we study the issue of unitarity of this massive gauge model. Firstly, we provide a short review how to discuss the unitarity making use of the BRST charge. Afterwards we make a detailed study of the most general version of our action, and we come to the conclusion that the model is not unitary, as we are unable to remove all the negative norm states from the physical spectrum in a consistent way., Comment: 36 pages

We show the renormalizability of a Lagrangian of nucleons and pions interacting via a pseudoscalar coupling in the presence of a medium. We extend the proof to the effective Lagrangian obtained from the previous one through the functional integration over the fermionic fields. Notably in the latter case the renormalization takes place within each order of the corresponding loop expansion. This result is of significance in view of the connection between the loop expansion and the conventional many-body approximation methods.