Polymer and Fock representations for a scalar field

Abhay Ashtekar, Jerzy Lewandowski, Hanno Sahlmann

Research output: Contribution to journalArticlepeer-review

103 Scopus citations


In loop quantum gravity, matter fields can have support only on the 'polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states cannot refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background-independent operator algebras and Hilbert spaces. Second, to make contact with low-energy physics, one has to relate this 'polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.

Original languageEnglish (US)
Pages (from-to)L11-L21
JournalClassical and Quantum Gravity
Issue number1
StatePublished - Jan 7 2003

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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