Polymer quantization and advanced gravitational wave detector

Abstract

We investigate the observable consequences of Planck scale effects in the advanced gravitational wave detector by polymer quantizing the optical field in the arms of the interferometer. For large values of polymer energy scale, compared to the frequency of photon field in the interferometer arms, we consider the optical field to be a collection of infinite decoupled harmonic oscillators, and construct a new set of approximated polymer-modified creation and annihilation operators to quantize the optical field. Employing these approximated polymer-modified operators, we obtain the fluctuations in the radiation pressure on the end mirrors and the number of output photons. We compare our results with the standard quantization scheme and corrections from the Generalized Uncertainty Principle.

Quantum Groups and Polymer Quantum Mechanics

“…For other approaches see also [17]. Despite the rich literature, the general issue remains still completely open, and part of the focus is shifting on the so-called polymer quantization (PQ) [18,19] (that is a slightly simplified quantization inspired by LQG, that is reliable and heavily used [20][21][22][23][24][25][26]) and to its application to finite degrees of freedom systems, polymer quantum mechanics (PQM) [27][28][29]. PQ is based on the polymer representation of the Weyl-Heisenberg (WH) algebra, which is a non-regular representation, inequivalent to the standard Schrödinger or Fock-Bargmann representations [30].…”