Quantum theory of electromagnetic fields in a cosmological quantum spacetime

Abstract

The theory of quantum fields propagating on an isotropic cosmological quantum spacetime is reexamined by generalizing the scalar test field to an electromagnetic (EM) vector field. For any given polarization of the EM field on the classical background, the Hamiltonian can be written in the form of the Hamiltonian of a set of decoupled harmonic oscillators, each corresponding to a single mode of the field. In transition from the classical to quantum spacetime background, following the technical procedure given by Ashtekar et al. [Phys. Rev. D 79, 064030 (2009)], a quantum theory of the test EM field on an effective (dressed) spacetime emerges. The nature of this emerging dressed geometry is independent of the chosen polarization, but it may depend on the energy of the corresponding field mode. Specifically, when the backreaction of the field on the quantum geometry is negligible (i.e., a test field approximation is assumed), all field modes probe the same effective background independent of the mode's energy. However, when the backreaction of the field modes on the quantum geometry is significant, by employing a Born-Oppenheimer approximation, it is shown that a rainbow (i.e., a mode-dependent) metric emerges. The emergence of this mode-dependent background in the Planck regime may have a significant effect on the creation of quantum particles. The production amount on the dressed background is computed and is compared with the familiar results on the classical geometry.

Cosmological Particle Production in Quantum Gravity

“…Nevertheless, if we suppose that the approximation in Equation ( 28) is valid, the presence of the backreaction would lead to a modification of the total state as Ψ = Ψ o ⊗ ψ + δΨ (cf. [18,20]). Taking into account such modification, the dispersion relation of the field, propagating on the emergent effective geometry, will be modified such that the local Lorentz symmetry becomes violated.…”

“…Further phenomenological consequences and observational predictions of LQC can be found, e.g., in Refs. [17][18][19][20][21][22][23][24][25][26][27][28][29], respectively.…”

“…For massive modes, quantum gravity effects may induce a small deviation from the initial isotropy [19,24]. If the backreaction is considered, other properties, such as emerging a mode-dependent background, can raise, which leads to the violation of the local Lorentz symmetry [18,20]. Even in the absence of the backreaction between the states of the gravity and matter fields, a backreaction effect may arise due to the gravitational particle production, which can challenge the validity of the test field approximations employed in the dressed metric scenario [22].…”

Quanton Fields: Evolution and Degrees of Freedom

“…Here , an integrated approach is provided for the treatment of electromagnetic Field as as a quantized phenomena which was attempted previously [10], [11] The formulation of electromagnetic waves in terms of energy fields depends on the system of units, under the (Esu) system volumetric electromagnetic…”

Rainbow-Like Black-Hole Metric from Loop Quantum Gravity

“…(19) and (47), inspired by this approach. Alternative formulations of the rainbow gravity initial proposal have been proposed [74][75][76][77][78][79][80][81][82] and the issue is still under debate. Since the exact form of the semiclassical spacetime description from quantum gravity is not known yet, we should rely on phenomenological possibilities driven by deformation functions, like the HDA approach or rainbow gravity models, for instance.…”