Spin foam quantization and anomalies

Martin Bojowald, Alejandro Perez

Research output: Contribution to journalArticle

30 Citations (Scopus)

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

Fingerprint

foams
anomalies
requirements
fixing
constrictions
algebra
derivation
gravitation
formulations

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

Cite this

Bojowald, Martin ; Perez, Alejandro. / Spin foam quantization and anomalies. In: General Relativity and Gravitation. 2010 ; Vol. 42, No. 4. pp. 877-907.
@article{90f40391316449ca90c00b86f9efafd7,
title = "Spin foam quantization and anomalies",
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.",
author = "Martin Bojowald and Alejandro Perez",
year = "2010",
month = "4",
day = "1",
doi = "10.1007/s10714-009-0892-9",
language = "English (US)",
volume = "42",
pages = "877--907",
journal = "General Relativity and Gravitation",
issn = "0001-7701",
publisher = "Springer New York",
number = "4",

}

Spin foam quantization and anomalies. / Bojowald, Martin; Perez, Alejandro.

In: General Relativity and Gravitation, Vol. 42, No. 4, 01.04.2010, p. 877-907.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Spin foam quantization and anomalies

AU - Bojowald, Martin

AU - Perez, Alejandro

PY - 2010/4/1

Y1 - 2010/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77950460691&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950460691&partnerID=8YFLogxK

U2 - 10.1007/s10714-009-0892-9

DO - 10.1007/s10714-009-0892-9

M3 - Article

AN - SCOPUS:77950460691

VL - 42

SP - 877

EP - 907

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

SN - 0001-7701

IS - 4

ER -