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The effects of quantum corrections to a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary are considered in the context of a renormalisation procedure. The renormalisation of the…
For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary…
Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold…
Einstein-like Lagrangian field theory is developed to describe elastic solid containing dislocations with finite-sized core. The framework of the Riemann-Cartan geometry in three dimensions is used, and the core self-energy is expressed by…
The method of effective field theories (EFTs) is developed for the scattering of two particles at wavelengths which are large compared to the range of their interaction. It is shown that the renormalized EFT is equivalent to the effective…
There are reasons to believe that the Standard Model is only an effective theory, with new Physics lying beyond it. Supersymmetric extensions are one possibility: they address some of the Standard Model's shortcomings, such as the…
We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on $U(1)^4$ is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of…
We explore the adiabatic particle excitations of an interacting field in a cosmological background. By following the time-evolution of the quantum state corresponding to the particle excitation, we show how the basic properties…
We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows full control over the finite parts of the counterterms and provides explicit…
The previously developed renormalizable perturbative 1/N-expansion in higher dimensional scalar field theories is extended to gauge theories with fermions. It is based on the $1/N_f$-expansion and results in a logarithmically divergent…
The usual renormalization procedure for the variational approximation with a trial Gaussian ansatz for the $\lap$ model in 3+1 dimensions is re-analysed as a departing framework for the investigation of the parameters of the model. The…
In a previous paper it was shown how to calculate the ground-state energy density $E$ and the $p$-point Green's functions $G_p(x_1,x_2,...,x_p)$ for the $PT$-symmetric quantum field theory defined by the Hamiltonian density…
We study unitarity and renormalizability in the Lifshitz scalar field theory, which is characterized by an anisotropic scaling between the space and time directions. Without the Lorentz symmetry, both the unitarity and the renormalizability…
The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential…
We reevaluate the status of the gauge principle and reposition it as an intermediary structure dependent on the initial conditions we endow on our theory. We explore how the gauge symmetry manifests in the context of basic quantum…
We apply renormalisation-group methods to two-body scattering by a combination of known long-range and unknown short-range potentials. We impose a cut-off in the basis of distorted waves of the long-range potential and identify possible…
In modified gravity, the one-loop matter power spectrum exhibits an ultraviolet divergence as shown in the framework of the degenerate higher-order scalar-tensor theory. To address this problem, we extend the effective field theory of large…
We define the renormalization group flow for a renormalizable interacting quantum field in curved spacetime via its behavior under scaling of the spacetime metric, $\g \to \lambda^2 \g$. We consider explicitly the case of a scalar field,…
The effect of gravitational tidal forces on renormalized quantum fields propagating in curved spacetime is investigated and a generalisation of the optical theorem to curved spacetime is proved. In the case of QED, the interaction of tidal…
A certain pattern of divergence of perturbative expansions in quantum field theories, related to their small and large momentum behaviour, is known as renormalons. We review formal and phenomenological aspects of renormalon divergence. We…