Sage Interactions - Loop Quantum Gravity

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Quantum tetrahedron volume, area and angle eigenvalues

by David Horgan.

In this interact I calculate the angle, area and volume for a quantum tetrahedron The angle is found using the expression: theta = arccos((j3*(j3+1)-(j1*(j1+j1)-j2*(j2+1))/(2*sqrt(j1*(j1+j1)*j2*(j2+1)))) The area is found using the expression: A=sqrt(j1*(j1+1)) The volume is fund using the expression V^2 =M = 2/9(real antisymmetrix matrix)

Values of constants gamma is Immirzi parameter gamma =numerical_approx( ln(2)/(pi*sqrt(2))) #G = 6.63*10^-11 hbar= (1.61619926*10^-35)/(2*pi) lp is the planck length lp3=6*10^-104 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, area 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.