Laurent Freidel and Etera R Livine 2006 Class. Quantum Grav. 23 2021 doi:10.1088/0264-9381/23/6/012
Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory
Laurent Freidel1,2 and Etera R Livine1
Show affiliationsWe study the no-gravity limit GN → 0 of the Ponzano–Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with the Hadamard propagator) expressed as an Abelian spin foam model. We show how the GN expansion of the Ponzano–Regge amplitudes can be resummed. This leads to the conclusion that the effective dynamics of quantum particles coupled to quantum 3D gravity can be expressed in terms of an effective new non-commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagators.
- PACS
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04.60.Pp Loop quantum gravity, quantum geometry, spin foams
04.62.+v Quantum fields in curved spacetime
- MSC
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81T75 Noncommutative geometry methods (See also 46L85, 46L87, 58B34)
- Subjects
- Dates
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Issue 6 (21 March 2006)
Received 11 November 2005
Published 6 March 2006
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Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory
Laurent Freidel and Etera R Livine 2006 Class. Quantum Grav. 23 2021
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