Quantum group symmetry and discrete scale invariance: Spectral aspects

TL;DR

This paper explores the spectral properties of q-deformed models related to discrete scale invariance, revealing unique spectral behaviors, log-periodic functions, and q-deformed zeta functions with applications to discretely self-similar space-times.

Contribution

It establishes a connection between q-deformation, discrete scale invariance, and spectral analysis, introducing q-deformed zeta functions and analyzing their implications.

Findings

Models exhibit discrete scale invariance after regularization.

Spectra characterized by functional and q-periodic behaviors.

Identification of q-deformed zeta functions with complex poles.

Abstract

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 scale invariant. We discuss the consequences of their distinctive spectra, characterized by functional behavior. The role of log-periodic behavior and q-periodic functions is examined, and we show how q-deformed zeta functions, characterized by complex poles, appear. As an application, we discuss one-loop effects in discretely self-similar space-times.