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The Zero Temperature Heisenberg Ferromagnet as a Field Theory

  • Daniel A. Dubin

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. †.
    R. F. Streater, Comm. Math. Phys. (1967).Google Scholar
  2. *.
    D. A. Dubin, Fock Space Formulation of the Ferromagnet, ICTP/67/36 (1967).Google Scholar
  3. *.
    D. A. Dubin and R. F. Streater, Nuovo Cimento 50: 154 (1967).CrossRefGoogle Scholar
  4. *.
    R. F. Streater, Current Commutation Relations and Continuous Tensor Products, ICTP/67/20 (1967).Google Scholar

Copyright information

© Plenum Press 1969

Authors and Affiliations

  • Daniel A. Dubin
    • 1
  1. 1.Imperial CollegeLondonEngland

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