Polymer quantization on compact spaces yields finite graph Hilbert spaces whose exact ring and box spectra recover Schrödinger QM as lattice spacing vanishes.
The propagator in polymer quantum field theory
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abstract
We study free scalar field theory on flat spacetime using a background independent (polymer) quantization procedure. Specifically we compute the propagator using a method that takes the energy spectrum and position matrix elements of the harmonic oscillator as inputs. We obtain closed form results in the infrared and ultraviolet regimes that give Lorentz invariance violating dispersion relations, and show suppression of propagation at sufficiently high energy.
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Polymer quantum mechanics on compact configuration spaces
Polymer quantization on compact spaces yields finite graph Hilbert spaces whose exact ring and box spectra recover Schrödinger QM as lattice spacing vanishes.