Sage Interactions - Loop Quantum Gravity
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Contents
Quantum tetrahedron volume and angle eigenvalues
by David Horgan.
Enter the four J values into the input boxes. The values k range from kmin to kmax in integer steps. The dimension d of the Hilbert space H4, d = kmax - kmin + 1. we have kmin = max(|j1-j2|,|j3 -j4|)and kmax = min(j1+j2,j3 +j4). The the dimension of the hilbert space is given by d = kmax -kmin + 1. The volume matrix V^2 =M = 2/9(real antisymmetrix matrix). The spins must satisfy (j1+j2)<= (j3+j4)- the triangle inequality. Reference: Bohr-Sommerfeld Quantization of Space by Eugenio Bianchi and Hal M. Haggard. Reference: Shape in an atom of space: exploring quantum geometry phenomenology by Seth A. Major.
Research Blog: http://quantumtetrahedron.wordpress.com
Given the values of J1, J2, J3 and J4 this interact calculates the volume and angle eigenvalues of a quantum tetrahedron.
Quantum tetrahedron Area Operator eigenvalues
by David Horgan.
Given the values of J1, J2, J3 and J4 this interact calculates the area eigenvalues of a quantum tetrahedron.