Alejandro Corichi et al 2007 Class. Quantum Grav. 24 1495 doi:10.1088/0264-9381/24/6/008
Alejandro Corichi1,2,3, Tatjana Vukašinac4 and José A Zapata1
Show affiliationsIn this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested Schrödinger quantum mechanics. The kinematical cornerstone of our framework is the so-called polymer representation of the Heisenberg–Weyl (HW) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schrödinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.
Issue 6 (21 March 2007)
Received 19 October 2006, in final form 25 January 2007
Published 6 March 2007
Alejandro Corichi et al 2007 Class. Quantum Grav. 24 1495
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