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| print "Angle eigenvalue in radians=",(d8) | d8a=numerical_approx(d8, digits=4) angle = numerical_approx(d8*180/pi, digits=4) print 'angle between faces 1 and 2 in quantum tetrahedron = ',d8a, 'radians' print 'angle between faces 1 and 2 in quantum tetrahedron = ',angle, 'degrees' |
Sage Interactions - Loop Quantum Gravity
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Contents
Quantum tetrahedron volume 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,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.