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 language | English (US) |
|---|---|
| Pages (from-to) | 877-907 |
| Number of pages | 31 |
| Journal | General Relativity and Gravitation |
| Volume | 42 |
| Issue number | 4 |
| DOIs | |
| State | Published - Apr 1 2010 |
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All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)
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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 journal › Article
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 -