Related papers: Scale Setting for Self-consistent Backgrounds
We consider a massive scalar field living on the recently found exact quantum space-time corresponding to vacuum spherically symmetric loop quantum gravity. The discreteness of the quantum space time naturally regularizes the scalar field,…
A fundamental element of scale-dependent gravity is the scale-setting procedure. We present a new covariant expression to set the scale that arises when examining the field equations. Considering the renormalization group equations and…
The scale dependent effective average action for quantum gravity complies with the fundamental principle of Background Independence. Ultimately the background metric it formally depends on is selected self-consistently by means of a…
We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…
We examine the question of scale vs. conformal invariance for the linearized Einstein-Hilbert action, which describes the IR fixed point of quantum gravity. In $D = 4$, although the action is not conformally invariant in the usual sense, we…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
It is argued that the ambiguity introduced by the renormalization in the effective action of a four-dimensional renormalizable quantum field theory is at most a local polynomial action of canonical dimension four. The allowed ambiguity in…
New equations governing the scale transformation behaviors of a QFT with underlying structures are derived. These equations, with their several equivalent versions, can yield some new and significant insights and results that are difficult…
In the mathematically rigorous analysis of semiclassical Einstein's equations, the renormalisation of the stress-energy tensor plays a crucial role. We address such a topic in the case of a scalar field with both arbitrary mass and coupling…
The majority of renormalizable field theories possessing the scale invariance at the classical level exhibits the trace anomaly once quantum corrections are taken into account. This leads to the breaking of scale and conformal invariance.…
Using Schwinger's quantum action principle, dispersion relations are obtained for neutral scalar mesons interacting with bi-local sources. These relations are used as the basis of a method for representing the effect of interactions in the…
Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…
Quantum gravity can determine the dependence of gauge couplings in a scalar field, which is related to possible fifth forces and time varying fundamental "constants". This prediction is based on the scaling solution of functional flow…
We present a novel equivalence between scale-dependent gravity and scalar-tensor theories that have only a single scalar field with a canonical kinetic term in the Einstein frame and a conformal coupling to the metric tensor. In particular,…
A framework is proposed that allows to write down field theories with a new energy scale while explicitly preserving Lorentz invariance and without spoiling the features of standard quantum field theory which allow quick calculations of…
In recent papers it has been observed that non-Hermitian Hamiltonians, such as those describing $ig\phi^3$ and $-g\phi^4$ field theories, still possess real positive spectra so long as the weaker condition of ${\cal PT}$ symmetry holds.…
We study the background scale independence in single-metric approximation to the functional renormalization group equation (FRGE) for quantum gravity and show that it is possible to formulate it without using higher-derivative gauge fixing…
The Pauli--Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential…