Oriti continued

One main way of understanding GFTs is as a second quantized field theory of spin

network vertices, each corresponding to a quantum  of the field φ  and labelled by the d  group or Lie algebra elements, constructed in such a way that its quantum states are generic superpositions of spin networks and its Feynman diagrams are spin foams. For any given spin foam model, there exists a choice of GFT action (thus, a specific GFT model), such that the corresponding Feynman amplitudes are the chosen spin foam amplitudes. It can be seen, therefore, as a possible (second quantized) incarnation of the LQG programme. And: Using the dual simplicial formulation of spin networks and spin foams,  GFTs can also be understood as a second quantization of simplicial geometry, in which simplices can be created and annihilated in fundamental interaction processes, as well as change size and shape (with group or Lie algebra elements characterizing areas of triangles, discrete curvature, etc).

The main advantages compared to other formulations of LQG or spin foams are first of all that GFTs offer a complete  definition of the quantum dynamics, e.g. a clear prescription for the weights to be used in the sum over spin foams and for how this should be generated; second, that one can take advantage of more or less standard QFT tools in studying the theory, despite the fully background independent context (from the point of view of physical spacetime). This in particular would be a key asset to study the physics of large numbers of LQG degrees of freedom (large spin networks and spin foams), e.g. using powerful tools like the renormalization group.


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