Path integral representation Clause Samples

Path integral representation. Σ A spin foam σ is a 2-complex Γ with a representation jf of the gauge group G associated to each face and an intertwiner ie associated to each edge [58]. The gauge group can be either SO(4) or SO(1, 3) for the 4-dimensional models; it is SO(1, 2) or SO(3) in 3 spacetime dimensions; usually they are replaced with the corresponding universal covering groups. A Spin Foam Model [59] is de ▇▇▇, at least formally, by the partition function Z = w(Γ)Z[Γ] (129) where the amplitude associated to the spin foam Γ is Z[Γ] = Σ Y Af (jf ) Y Ae(jf , ie) Y ▇▇(jf , ie) . (130) jf ,ie
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