Background independent quantization and wave propagation

Abstract

We apply a type of background independent "polymer" quantization to a free scalar field in a flat spacetime. Using semi-classical states, we find an effective wave equation that is both nonlinear and Lorentz invariance violating. We solve this equation perturbatively for several cases of physical interest, and show that polymer corrections to solutions of the Klein-Gordon equation depend on the amplitude of the field. This leads to an effective dispersion relation that depends on the amplitude, frequency and shape of the wave-packet, and is hence distinct from other modified dispersion relations found in the literature. We also demonstrate that polymer effects tend to accumulate with time for plane-symmetric waveforms. We conclude by discussing the possibility of measuring deviations from the Klein-Gordon equation in particle accelerators or astrophysical observations.

15 pages, minor revision to match PRD version

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Cited by in corpus (26)

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• Generalized uncertainty principles and localization in discrete space
• The propagator in polymer quantum field theory
• Non-singular inflationary universe from polymer matter
• High energy modifications of blackbody radiation and dimensional reduction
• Propagators in Polymer Quantum Mechanics
• Minisuperspace models as infrared contributions
• Ultraviolet behavior in background independent quantum field theory
• Propagation of quantum gravity-modified gravitational waves on a classical FLRW spacetime
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• Gravitational collapse of quantum matter
• Singularity resolution from polymer quantum matter
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• Natural Inflation from Polymer Quantization
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• Polymer quantization and advanced gravitational wave detector
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• On plane gravitational waves in real connection variables
• Localization and diffusion in polymer quantum field theory
• Frustration of resonant preheating by exotic kinetic terms
• Singularity resolution by lattice shifts in discretised quantum mechanics
• A symplectic geometric origin of universal quartic modified dispersion relations
• Smoothed quantum fluctuations and CMB observations