Skip to main content

Advertisement

Table 2 System algebras t M (L) of translation-invariant systems with 1L6 spins and interaction lengths of less than M . Refer also to Theorem 25 for the structure of t L (L)

From: A dynamic systems approach to fermions and their relation to spins

M L = 1 2 3 4
1 su(2) su(2) su(2) su(2)
2   su(3)+u(1) su(4)+ i = 1 2 su(2)+u(1) su(6)+su(4)+ i = 1 2 su(2)+u(1)
3    su(4)+ i = 1 2 su(2)+ i = 1 2 u(1) su(6)+su(4)+ i = 1 2 su(3)+ i = 1 3 u(1)
4     su(6)+su(4)+ i = 1 2 su(3)+ i = 1 3 u(1)
M L = 5 6
1 su(2) su(2)
2 su(8)+ i = 1 4 su(6)+u(1) su(14)+ i = 1 2 su(11)+su(10)+ i = 1 2 su(9)+u(1)
3 su(8)+ i = 1 4 su(6)+ i = 1 2 u(1) su(14)+ i = 1 2 su(11)+su(10)+ i = 1 2 su(9)+ i = 1 3 u(1)
4 su(8)+ i = 1 4 su(6)+ i = 1 4 u(1) su(14)+ i = 1 2 su(11)+su(10)+ i = 1 2 su(9)+ i = 1 4 u(1)
5 su(8)+ i = 1 4 su(6)+ i = 1 4 u(1) su(14)+ i = 1 2 su(11)+su(10)+ i = 1 2 su(9)+ i = 1 5 u(1)
6   su(14)+ i = 1 2 su(11)+su(10)+ i = 1 2 su(9)+ i = 1 5 u(1)