Related papers: Physics Fun with Discrete Scale Invariance
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…
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…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…
Generally, quantum field theories can be thought as deformations away from conformal field theories. In this article, with a simple bottom up model assumed to possess a holographic description, we study a putative large N quantum field…
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…
Quantum field theory offers physicists a tremendously wide range of application; it is both a language with which a vast variety of physical processes can be discussed and also it provides a model for fundamental physics, the so-called…
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
We re-consider the quantum mechanics of scale invariant potentials in two dimensions. The breaking of scale invariance by quantum effects is analyzed by the explicit evaluation of the phase shift and the self-adjoint extension method. We…
We give a modern geometric viewpoint on anomalies in quantum field theory and illustrate it in a 1-dimensional theory: supersymmetric quantum mechanics. This is background for the resolution of worldsheet anomalies in orientifold…
We analyze, from a canonical quantum field theory perspective, the problem of one-dimensional particles with three-body attractive interactions, which was recently shown to exhibit a scale anomaly identical to that observed in…
I investigate two discrete models of random geometries, namely simplicial quantum gravity and quantum string theory. In four-dimensional simplicial quantum gravity, I show that the addition of matter gauge fields to the model is capable of…
Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and can be used to systematically prevent…
We summarize basic features of quantum field theories with discrete symmetry $\mathbb{Q}/\mathbb{Z}$ (possibly higher form, global or gauged). The classification of representations and anomalies is quite rich and involves the ring of…
We study the consistency of having Lorentz invariance as a low energy approximation within the quantum field theory framework. A model with a scalar and a fermion field is used to show how a Lorentz invariance violating high momentum scale,…
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams…
We give simple examples of weakly coupled or free quantum mechanical systems that exhibit scale invariance with an anomalous dimension for a conserved current. In these models scaling as an exact symmetry only emerges in a large N limit,…
Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in…
We study analytical aspects of a generic q-deformation with q real, by relating it with discrete scale invariance. We show how models of conformal quantum mechanics, in the strong coupling regime and after regularization, are also discrete…