New spinfoam vertex for quantum gravity

By Etera R. Livine, Simone Speziale. 2007

389 citations recorded by the source corpus.

We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the 15j symbol, in a particular basis constructed using SU(2) coherent states. This basis makes the geometric interpretation of the variables transparent: they are the vectors normal to the triangles within each tetrahedron. We study the condition under which these states can be considered semiclassical, and we show that the semiclassical ones dominate the evaluation of quantum correlations. Finally, we describe how the constraints reducing BF to gravity can be directly written in terms of the new variables, and how the semiclassicality of the states might improve understanding the correct way to implement the constraints.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8bf82fe60267ef69989459f7bcca72202335ba87

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Citations in the corpus

Complete LQG propagator: Difficulties with the Barrett-Crane vertex (2007, background): “Recently, a vertex amplitude that modifies the BC amplitude, and which addresses precisely the problems that we find here, has been proposed [16, 17 ], see also [18].”
Flipped spinfoam vertex and loop gravity (2007, background): “raints, and (iii) the Gauss constraint. (ii) Livine and Speziale have found an independent derivation of the vertex proposed here [45], based on the use of the coherent states they have introduced in [18]. (iii) The discreteness introduced by the Regge triangulation should not be confused with the q”
Polyhedra in loop quantum gravity (2010, background): “ection. 8Notice that an ordering can be chosen so that the area is exactly Aˆ i = 8πγL 2 P ji. 17 4.2 Coherent intertwiners and semiclassical polyhedra Coherent intertwiners for HF were introduced in [8] and furtherly developed in [9, 23] (for previous related work, see [28]). These Livine-Speziale ”
Colored Group Field Theory (2009, positive): “This line of research has been explored in [19–23], to define more realistic GFT’s whose semiclassical limit [24,25] exhibits the expected behavior.”
The Spin-Foam Approach to Quantum Gravity (2012, methodology): “The coherent intertwiner basis relevant for the definition of spin foams and the 4d quantum gravity amplitude was also derived by Livine and Speziale in [246].”
On the semiclassical limit of 4d spin foam models (2008, methodology): “More recently, two new techniques for constructing spin foam models were introduced that open the way to a resolution of this difficulty: the coherent state method [23], based on integrals over coherent states on the group, and a new way of implementing the simplicity constraints [24].”
A new spin foam model for 4D gravity (2007, methodology): “To this end, we have further developed the new geometric perspective on the simplicity constraints, as well as the new geometrical interpretation suggested by the use of coherent states in [17].”
Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude (2009, methodology): “Furthermore, we want to describe tetrahedra with three-dimensional rotational symmetry and the coherent intertwiners are thus constructed by integrating over all spatial directions the tensor product of four coherent states as in [ 12 ]:”
Lorentzian spin foam amplitudes: graphical calculus and asymptotics (2009, background): “otic analysis are those determined by coherent states in each SU(2) representation [25]. These states have the property that a deﬁnite geometry emerges for each tetrahedron in the semiclassical limit [36]. A coherent state [37] is determined by a spinor ξ∈ C2. The coherent state in Vk is the tensor ”
Zakopane lectures on loop gravity (2011, background): “Here I describe the “holomorphic" coherent states, developed by a number of people [84, 85, 52, 86, 87] and recently discussed in detail by Bianchi-Magliaro-Perini [55], as well as the “semi coherent" states of Livine-Speziale (LS) [17].”