# The Zero Temperature Heisenberg Ferromagnet as a Field Theory

## Abstract

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.

## Keywords

Unbounded Operator Fixed Integer Wightman Function Algebraic Framework Space Translation## Preview

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## References

- †.R. F. Streater,
*Comm. Math. Phys*. (1967).Google Scholar - *.D. A. Dubin,
*Fock Space Formulation of the Ferromagnet*, ICTP/67/36 (1967).Google Scholar - *.
- *.R. F. Streater,
*Current Commutation Relations and Continuous Tensor Products*, ICTP/67/20 (1967).Google Scholar