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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


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html('<h3>Quantum tetrahedron Volume and Angle Eigenvalues</h3>')
html('Enter the four J values into the input boxes')
html('k values k ranges from kmin to kmax in integer steps')
html('The dimension d of the Hilbert space H4, d = kmax - kmin + 1')
html('kmin = max(|j1-j2|,|j3 -j4|) kmax = min(j1+j2,j3 +j4)')
html('The the dimension of the hilbert space is given by d = kmax -kmin + 1')
html('V^2 =M = 2/9(real antisymmetrix matrix))')
html('Spins must satisfy (j1+j2)<= (j3+j4)')
html('Reference: Bohr-Sommerfeld Quantization of Space by Eugenio Bianchi and Hal M. Haggard ')
html('Reference: Shape in an atom of space: exploring quantum geometry phenomenology by Seth A. Major ')

Sage Interactions - Loop Quantum Gravity

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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 volume and angle eigenvalues of a quantum tetrahedron.

interact/Loop Quantum Gravity (last edited 2019-04-06 16:42:59 by chapoton)