mirror of
https://github.com/triqs/dft_tools
synced 2024-11-01 19:53:45 +01:00
39 lines
1.1 KiB
Plaintext
39 lines
1.1 KiB
Plaintext
Anticommutators:
|
|
{ 1*C^+(1,0) , 1*C(1,0) } = 1
|
|
{ 1*C^+(1,0) , 1*C(2,0) } = 0
|
|
{ 1*C^+(1,0) , 1*C(3,0) } = 0
|
|
{ 1*C^+(2,0) , 1*C(1,0) } = 0
|
|
{ 1*C^+(2,0) , 1*C(2,0) } = 1
|
|
{ 1*C^+(2,0) , 1*C(3,0) } = 0
|
|
{ 1*C^+(3,0) , 1*C(1,0) } = 0
|
|
{ 1*C^+(3,0) , 1*C(2,0) } = 0
|
|
{ 1*C^+(3,0) , 1*C(3,0) } = 1
|
|
Commutators:
|
|
[ 1*C^+(1,0) , 1*C(1,0) ] = -1 + 2*C^+(1,0)C(1,0)
|
|
[ 1*C^+(1,0) , 1*C(2,0) ] = 2*C^+(1,0)C(2,0)
|
|
[ 1*C^+(1,0) , 1*C(3,0) ] = 2*C^+(1,0)C(3,0)
|
|
[ 1*C^+(2,0) , 1*C(1,0) ] = 2*C^+(2,0)C(1,0)
|
|
[ 1*C^+(2,0) , 1*C(2,0) ] = -1 + 2*C^+(2,0)C(2,0)
|
|
[ 1*C^+(2,0) , 1*C(3,0) ] = 2*C^+(2,0)C(3,0)
|
|
[ 1*C^+(3,0) , 1*C(1,0) ] = 2*C^+(3,0)C(1,0)
|
|
[ 1*C^+(3,0) , 1*C(2,0) ] = 2*C^+(3,0)C(2,0)
|
|
[ 1*C^+(3,0) , 1*C(3,0) ] = -1 + 2*C^+(3,0)C(3,0)
|
|
|
|
Algebra:
|
|
x = 1*C(0,0)
|
|
y = 1*C^+(1,0)
|
|
-x = -1*C(0,0)
|
|
x + 2.0 = 2 + 1*C(0,0)
|
|
2.0 + x = 2 + 1*C(0,0)
|
|
x - 2.0 = -2 + 1*C(0,0)
|
|
2.0 - x = 2 + -1*C(0,0)
|
|
3.0*y = 3*C^+(1,0)
|
|
y*3.0 = 3*C^+(1,0)
|
|
x + y = 1*C^+(1,0) + 1*C(0,0)
|
|
x - y = -1*C^+(1,0) + 1*C(0,0)
|
|
(x + y)*(x - y) = 2*C^+(1,0)C(0,0)
|
|
|
|
N^3:
|
|
N = 1*C^+(0,dn)C(0,dn) + 1*C^+(0,up)C(0,up)
|
|
N^3 = 1*C^+(0,dn)C(0,dn) + 1*C^+(0,up)C(0,up) + 6*C^+(0,dn)C^+(0,up)C(0,up)C(0,dn)
|