Applications of polymeric quantisation

Abstract

Polymer quantisation is a background independent quantisation scheme inspired by loop quantum gravity. Under this quantisation scheme, it predicts that space is discretised and changes in multiples of a fundamental length scale ?. As a result, the momentum operator is not well-defined. However, a new operator can be defined such that a Schr鰀inger-like equation can be retrieved. The solutions give rise to eigenspectra which are similar to the standard counterparts, with an additional correction term due to ?. We present the basic principles of the polymer representation and apply it to the harmonic oscillator to study the phenomenological implications of such solutions. In addition, we consider an ensemble of such oscillators and calculated the thermodynamical properties for systems that safisty the bosonic and fermionic statistics. The results presented may have physical significance at high energy scales or in exotic matter. � The Authors, published by EDP Sciences.