The Zero Temperature Heisenberg Ferromagnet as a Field Theory
We envision an infinite lattice in N dimensions whose points are isomorphic to ℒ⊗ N. At each lattice site there is a degree of freedom known as spin. The spin can take two values which we call ±½ħ. Hereafter ħ = 1, the natural units. A state of the system is given by specifying the spin (±½) at each lattice point together with an amplitude there, i.e., a real number at each site. The idealized interaction is given through a generally unbounded operator, the Hamiltonian, H, which is, in the algebraic framework, the generator of the time evolution automorphism. This simplified picture, together with a particular form for H, due originally to Heisenberg, is an idealization of the zero temperature ferromagnet where the crystal ions are frozen in place.
KeywordsUnbounded Operator Fixed Integer Wightman Function Algebraic Framework Space Translation
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