Related papers: Hidden and explicit quantum scale invariance
We explore the possibility that scale symmetry is a quantum symmetry that is broken only spontaneously and apply this idea to the Standard Model (SM). We compute the quantum corrections to the potential of the higgs field ($\phi$) in the…
It is known that scale invariance is broken in the developed hydrodynamic turbulence due to intermittency, substantiating complexity of turbulent flows. Here we challenge the concept of broken scale invariance by establishing a hidden…
The quest for finding self-consistent background solutions in quantum field theory is closely related to the way one decides to set the renormalization scale $k$. This freedom in the choice of the scale setting can lead to ambiguities and…
We provide a review on the physics associated with phase transitions in which continuous scale invariance is broken into discrete scale invariance. The rich features of this transition characterized by the abrupt formation of a geometric…
we show there exists a mathematically consistent framework in which the Renormalization Program can be understood in a natural manner. The framework does not require any violations of mathematical rigor usually associated with the…
Running couplings can be understood as arising from the spontaneous breaking of an exact scale invariance in appropriate effective theories with no dilatation anomaly. Any ordinary quantum field theory, even if it has massive fields, can be…
Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.
The concept of F-invariance, which previously arose in our analysis of the integral and half-integral quantum Hall effects, is studied in 2+2\epsilon spatial dimensions. We report the results of a detailed renormalization group analysis and…
With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…
The inverse scale factor, which in classical cosmological models diverges at the singularity, is quantized in isotropic models of loop quantum cosmology by using techniques which have been developed in quantum geometry for a quantization of…
This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between…
We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group…
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…
The theory of deconfined quantum critical points describes phase transitions at temperature T = 0 outside the standard paradigm, predicting continuous transformations between certain ordered states where conventional theory requires…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
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…
Discrete scale invariance, which corresponds to a partial breaking of the scaling symmetry, is reflected in the existence of a hierarchy of characteristic scales l0, c l0, c^2 l0,... where c is a preferred scaling ratio and l0 a microscopic…
The scale invariance of the coupling constant in the induced gauge theory due to its compositeness condition is demonstrated in the renormalization group flow of the finite-cutoff gauge theory at the leading order in 1/N, where N is the…
The triangle anomaly in massless and massive QED is investigated by adopting the symmetry-preserving loop regularization method proposed recently in \cite{LR}. The method is realized in the initial dimension of theory without modifying the…