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| The '''Barrett–Crane model''' is a model in [[quantum gravity]] which was defined using the [[Plebanski action]].<ref name=Barrett1998>{{citation
| | I'm Sommer (18) from Bregnano, Italy. <br>I'm learning French literature at a local university and I'm just about to graduate.<br>I have a part time job in a backery.<br><br>Also visit my web page - [http://Ommarelard.Mustafahosny.com/index.php?option=com_content&view=article&id=6988:2012-05-29-05-44-49&catid=5:trials&Itemid=18 Fifa 15 Coin Generator] |
| | author = Barrett, John W.; Louis Crane
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| | title = Relativistic spin networks and quantum gravity
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| | journal = J.Math.Phys. 39
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| | volume = 39
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| | pages = 3296–3302
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| | doi = 10.1063/1.532254
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| | year = 1998
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| |arxiv = gr-qc/9709028 |bibcode = 1998JMP....39.3296B }}</ref><ref name=Barrett>{{citation
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| | author = Barrett, John W.; Louis
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| Crane,
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| | title = A Lorentzian signature model for quantum general relativity
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| | journal = Classical and Quantum Gravity
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| | volume = 17
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| | doi = 10.1088/0264-9381/17/16/302
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| |arxiv = gr-qc/9904025 |bibcode = 2000CQGra..17.3101B }}</ref>
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| The <math>B</math> field in the action is supposed to be a <math>so(3, 1)</math>-valued [[2-form]], i.e. taking values in the [[Lie algebra]] of a [[special orthogonal group]]. The term
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| :<math>B^{ij} \wedge B^{kl}</math>
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| in the action has the same symmetries as it does to provide the [[Einstein-Hilbert action]]. But the form of
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| :<math>B^{ij}</math>
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| is not unique and can be posed by the different forms:
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| *<math>\pm e^i \wedge e^j</math>
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| *<math>\pm \epsilon^{ijkl} e_k \wedge e_l</math>
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| where <math>e^i</math> is the [[tetrad]] and <math>\epsilon^{ijkl}</math> is the [[antisymmetric symbol]] of the <math>so(3, 1)</math>-valued 2-form fields.
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| The Plebanski action can be constrained to produce the [[BF model]] which is a theory of no local [[degrees of freedom (physics and chemistry)|degrees of freedom]]. [[John W. Barrett]] and [[Louis Crane]] modeled the analogous constraint on the summation over [[spin foam]].
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| The Barrett–Crane model on spin foam quantizes the [[Plebanski action]], but its [[functional integration|path integral]] amplitude corresponds to the degenerate <math>B</math> field and not the specific definition
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| :<math>B^{ij} = e^i \wedge e^j</math>,
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| which formally satisfies the [[Einstein's field equation]] of [[general relativity]]. However, if analysed with the tools of [[loop quantum gravity]] the Barrett–Crane model gives an incorrect long-distance limit [http://arxiv.org/abs/0708.0883], and so the model is not identical to loop quantum gravity.
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| ==See also==
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| * [[EPRL model]]
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:Barrett-Crane model}}
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| [[Category:Loop quantum gravity]]
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| {{physics-stub}}
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I'm Sommer (18) from Bregnano, Italy.
I'm learning French literature at a local university and I'm just about to graduate.
I have a part time job in a backery.
Also visit my web page - Fifa 15 Coin Generator