Agradecimientos:
We would like to thank W Chojnacki, A Corichi, J Lewandowski, T Pawłowski, P Singh and M Varadarajan for their valuable comments. This work has been supported by the Spanish MICINN research grants FIS2009-11893, FIS2012-34379 and the Consolider-Ingenio 2010
Program CPAN (CSD2007-00042).
Proyecto:
Gobierno de España. FIS2009-11893 Gobierno de España. FIS2012-34379 Gobierno de España. CSD2007-00042
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 spectrumWe 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 and may have interesting consequences for the statistical mechanics of these models.[+][-]
