Band structure in the polymer quantization of the harmonic oscillator

  title={Band structure in the polymer quantization of the harmonic oscillator},
  author={G. J.FernandoBarbero and Jorge Prieto and Eduardo J S Villase{\~n}or},
  journal={Classical and Quantum Gravity},
We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies that the point spectrum consists of bands similar to the ones appearing in the treatment of periodic potentials. This feature of the spectrum of the polymeric harmonic oscillator may be relevant for the discussion of the polymer quantization of the scalar field… Expand

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