String quantization: Fock vs. LQG Representations

Abstract

We set up a unified framework to compare the quantization of the bosonic string in two approaches: One proposed by Thiemann, based on methods of loop quantum gravity, and the other using the usual Fock space quantization. Both yield a diffeomorphism invariant quantum theory. We discuss why there is no central charge in Thiemann's approach but a discontinuity characteristic for the loop approach to diffeomorphism invariant theories. Then we show the (un)physical consequences of this discontinuity in the example of the harmonic oscillators such as an unbounded energy spectrum. On the other hand, in the continuous Fock representation, the unitary operators for the diffeomorphisms have to be constructed using the method of Gupta and Bleuler representing the diffeomorphism group up to a phase given by the usual central charge.

19 pages

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Cited by in corpus (9)

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• Polymer state approximations of Schroedinger wave functions
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• Higher curvature counter terms cause the bounce in loop cosmology
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Canonical Analysis of Algebraic String Actions
• Equivalence of the self-dual and Nambu-Goto strings