Bounds on the polymer scale from gamma ray bursts

Abstract

The polymer representations, which are partially motivated by loop quantum gravity, have been suggested as alternative schemes to quantize the matter fields. Here we apply a version of the polymer representations to the free electromagnetic field, in a reduced phase space setting, and derive the corresponding effective (i.e., semiclassical) Hamiltonian. We study the propagation of an electromagnetic pulse and we confront our theoretical results with gamma ray burst observations. This comparison reveals that the dimensionless polymer scale must be smaller than 4×10−35 , casting doubts on the possibility that the matter fields are quantized with the polymer representation we employed.Loop quantum gravity (LQG) [1][2][3], which is a prominent quantum gravity candidate, has inspired alternative matter quantization methods, known as polymer representations [4][5][6][7][8]. These alternative methods resemble LQG in that they are nonperturbative and unitarily inequivalent to the Schrödinger representation. Also, the formal way the states and the fundamental operators are expressed in the polymer representations, mimics the cylindrical functions and the holonomy-flux algebra of LQG, respectively. Moreover, the polymer representations have been considered, by themselves, as interesting alternatives to the Schrödinger quantization [9][10][11][12].Notably, most works on the polymer representations of matter fields use scalar fields or do not make contact with experimental data [13][14][15][16][17][18][19]. In contrast, our goal is to study the empirical consequences of applying such a quantization scheme to the free electromagnetic field in the framework of Ref. 7. To that end, we polymer quantize the Maxwell theory and then use well-known methods to extract the corresponding effective dynamics.As it is well known, the electromagnetic field A ν (x), ν being a spacetime index, has a U (1) gauge symmetry and, to quantize it, we utilize a reduced phase space quantization (see, for example, Ref. 20). Furthermore, we work in the Minkowski spacetime with a global Cartesian coordinate frame where t represents the time index and i, j are spatial indices. We fix the gauge by taking A t = 0 = ∂ i A i , which can be consistently imposed when there are no sources [21, chapter 6.3]. In this case the action takes the formIn this work we use a metric with signature +2 and adopt natural units, i.e., Lorentz-Heaviside units with the additional conditions c = 1 = . we use the spacetime foliation associated with constant t hypersurfaces and denote the canonically conjugated momenta by E i , resulting inThe fact that no constraints arise reflects that there is no remaining gauge freedom.To properly implement the polymer quantization we turn to Fourier space. Notice, however, that a priori we cannot assume Lorentz invariance, and thus, we do not use the standard four-dimensional Fourier transform. Instead we only perform such a transformation on the spatial coordinates. Furthermore, to have a countable number of modes, we consider the system t...

Constraining the quantum gravity polymer scale using LIGO data

“…In almost all of them, the reported bound on the polymer scale was sensitive to the characteristic properties of the setup, for example in [38,39], by changing the number of particles and the characteristic length of the one-dimensional oscillator, a different bound on the polymer scale can be obtained, or in [40,41], different value for the number of particles, size of the system or barrier width, would result in different bound on the polymer parameter. Even in [10], which employs the same procedure for the mode decomposition of the electromagnetic fields, final bounds on the polymer scale depends on the selected value for the size of the decomposition box and the amplitude of the observed GRB, which shows a similar role to the parameter ℓ in our setup.…”

“…This method can be applied to both matter, e.g. GRBs [10] and spacetime or its perturbations themselves [11,12].…”

“…Expanding on this work, we have also calculated the alterations to the response of a Michelson-Morley-like GW observatory under the influence of polymer effects [12,13]. The polymer quantization model has also been applied to the propagation of gamma-ray bursts [10].…”

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].…”

Casimir effect in polymer scalar field theory

“…PQ has been used to study quantum gravitational effects upon simple quantum systems, such as the harmonic oscillator [5], the particle in a box [6], the diffraction in time [7], the tunneling phenomena [8], the Coulomb potential [9,10], the quantum bouncer [11] and within statistical thermodynamics [12], just to name a few. It * Electronic address: alberto.martin@nucleares.unam.mx has also been applied to the scalar field theory [13][14][15][16] and the electromagnetic field [17]. In this work we develop the area of polymer quantum field theory further by computing the Casimir pressure between two parallel conducting plates in a polymer scenario.…”