Related papers: On Scale Invariance and Anomalies in Quantum Mecha…
In this paper we address again the issue of the scale anomaly in quantum mechanical models with inverse square potential. In particular we examine the interplay between the classical and quantum aspects of the system using in both cases an…
An anomaly is said to occur when a symmetry that is valid classically becomes broken as a result of quantization. Although most manifestations of this phenomenon are in the context of quantum field theory, there are at least two cases in…
Scale invariance in quantum mechanics can be broken in several ways. A well-known example is the breakdown of continuous scale invariance to discrete scale invariance, whose typical realization is the Efimov effect of three-body problems.…
We study scale invariance at the quantum level (three loops) in a perturbative approach. For a scale-invariant classical theory the scalar potential is computed at three-loop level while keeping manifest this symmetry. Spontaneous scale…
We consider a generic scale invariant scalar quantum field theory and its symmetry breakdown. Based on the dimension counting identity, we give a concise proof that dilaton is exactly massless at the classical level if scale invariance is…
We discuss spontaneous symmetry breaking of dual (space and time) scale invariance in the context of turbulence.
We compute the classical and the quantum breaking of the dilatation current in the minimal Lorentz and CPT-violating quantum electrodynamics. At the classical level, scale symmetry is broken by the general mass term \bar{\psi}M\psi and the…
We argue that scale invariance is not anomalous in quantum field theory, provided it is broken cosmologically. We consider a locally scale invariant extension of the Standard Model of particle physics and argue that it fits both the…
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…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…
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…
A new version of the delta expansion is presented, which, unlike the conventional delta expansion, can be used to do nonperturbative calculations in a self-interacting scalar quantum field theory having broken symmetry. We calculate the…
A number of physical systems exhibit a particular form of asymptotic conformal invariance: within a particular range of distances, they are characterized by a long-range conformal interaction (inverse square potential), the absence of…
Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar $\phi$ in theories in…
Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At…
We review and expand upon recent work demonstrating that Weyl invariant theories can be broken "inertially," which does not depend upon a potential. This can be understood in a general way by the "current algebra" of these theories,…
Renormalization in quantum statistics in the presence of a charge associated to a spontaneously broken symmetry is discussed for the scalar field model. In contrast to the case of non-broken symmetry, the renormalization mass counterterm…
We propose a scheme leading to a non-perturbative definition of lattice field theories which are scale-invariant on the quantum level. A key idea of the construction is the replacement of the lattice spacing by a propagating dynamical field…
Scale invariant theories which contain maximal rank gauge field strengths (of $D$ indices in $D$ dimensions) are studied. The integration of the equations of motion of these gauge fields leads to the s.s.b. of scale invariance. The cases in…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…