Band structure in the polymer quantization of the harmonic oscillator Articles uri icon

publication date

  • July 2013

start page

  • 165011

issue

  • 16

volume

  • 30

International Standard Serial Number (ISSN)

  • 0264-9381

Electronic International Standard Serial Number (EISSN)

  • 1361-6382

abstract

  • 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 and may have interesting consequences for the statistical mechanics of these models.

keywords

  • backgroung indepent quantizations; periodic schrodinger-operators; quantum-mechanics; scalar field; representations; equiation; gravity; entropy; l2(br)