Paul Bird's Scientific Research

Why not expand LQG around a ground state? It makes more sense? psi(A) = Sum_loops exp(iA.dx) * Ground(A) In 2+1 dimensions Ground(A) might be for example the chern simons invariant. AdA+(2/3)A^A^A

Let us take a wave function of the metric at time T=0. Expanded around a flat space g  = n + h. Ψ[h] = a +  Ψ( x )h( x ,0) +  Ψ( x , y )h( x ,0)h( y ,0) + ..... The Wheeler-de-Witt equation should give a relation between the  Ψ s. Because g is a linear function of h, d/dh=d/dg. When expanded in terms of h, this has an infinite number of terms. This imposes very special constraints on  Ψ  to give it the right symmetries. (A similar thing happens in string theory). ((gg+gg-gg) d/dh( x ,0) d/dh( x ,0) + det(g)R[g] )   Ψ[h] = 0 This equation says how the wave function amplitudes are connected  be when 2 particles are in the same place.  If h^2 is approximately 0. Then h behaves like a gauge field. Part 2 ------- Lets take a different expansion g=exp(h) , det(g) = exp(Tr(h)) , delta h = da + db? Then this timer d/dg = g^-1 d/dh (  d/dh d/dh +  exp(Tr[h]+h+h-h)*(dh)^2 )   Ψ[h] = 0 ? Ψ(x) = exp(-x^2) = 1 - x^2 + x^4/2! +... int exp(-x^2) dx = sqrt(pi)  exp(-