Spin foam quantization and anomalies

Martin Bojowald, Alejandro Perez

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are left open to choice. Since their large-spin behavior determines the convergence properties of the state-sum, this gap has to be closed before any reliable conclusion about finiteness can be reached. It is shown that these amplitudes are directly related to the path integral measure and can in principle be derived from it, requiring detailed knowledge of the constraint algebra and gauge fixing. In a related manner, minimal requirements of background independence provide non trivial restrictions on the form of an anomaly free measure. Many models in the literature do not satisfy these requirements. A simple model satisfying the above consistency requirements is presented which can be thought of as a spin foam quantization of the Husain-Kuchař model.

Original languageEnglish (US)
Pages (from-to)877-907
Number of pages31
JournalGeneral Relativity and Gravitation
Volume42
Issue number4
DOIs
StatePublished - Apr 1 2010

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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