Related papers: Scale symmetry in classical and quantum mechanics
We generalize the standard first-order intertwining relationship of supersymmetric quantum mechanics in order to include simultaneous scaling transformations in both the original Hamiltonian and the intertwining operator. It is argued that…
In the context of quantum field theory, an anomaly exists when a theory has a classical symmetry which is not a symmetry of the quantum theory. This short exposition aims at introducing a new point of view, which is that the proper setting…
It is demonstrated that a nonrelativistic quantum scale anomaly manifests itself in the appearance of composite operators with complex scaling dimensions. In particular, we study nonrelativistic quantum mechanics with an inverse square…
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
There exist renormalisation schemes that explicitly preserve the scale invariance of a theory at the quantum level. Imposing a scale invariant renormalisation breaks renormalisability and induces new non-trivial operators in the theory. In…
We study the implications of scale invariance in four-dimensional quantum field theories. Imposing unitarity, we find that infinitely many matrix elements vanish in a suitable kinematical configuration. This vanishing is a nontrivial…
We construct an exactly solvable relativistic model that embeds the anomalous inverse-square interaction into a non-Hermitian Klein-Gordon field theory through a purely imaginary, scale-invariant scalar potential. The stationary field…
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…
Quantum anomalies are violations of classical scaling symmetries caused by quantum fluctuations. Although they appear prominently in quantum field theory to regularize divergent physical quantities, their influence on experimental…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
If scale invariance is a classical symmetry then both the Planck scale and the weak scale should emerge as quantum effects. We show that this can be realized in simple scale invariant theories with a hidden sector. The weak/Planck scale…
A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.
One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to…
It is the purpose of the present manuscript to emphasize those aspects that make the scalar sector with vacuum quantum numbers rather unique. Chiral symmetry is the basic tool for our study together with a resummation of Chiral Perturbation…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
Scale invariance supplemented by the requirement of the absence of new heavy particles may play an important role in addressing the hierarchy problem. We discuss how the Standard Model may become scale invariant at the quantum level above a…