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arXiv · 1208.5761

Generalized uncertainty principles and quantum field theory

Viqar Husain·Dawood Kothawala·Sanjeev S. Seahra
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Abstract

Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm βp^2$. The resulting quantum field theories have a rich fine scale structure. For small wavelength modes, the Green's function for $f_+$ exhibits a remarkable transition from Lorentz to Galilean invariance, whereas for $f_-$ such modes effectively do not propagate. For both cases Lorentz invariance is recovered at long wavelengths.

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Viqar Husain, Dawood Kothawala, Sanjeev S. Seahra. 2012-08-28. Generalized uncertainty principles and quantum field theory. https://doi.org/10.1103/physrevd.87.025014

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