Methods of Dynamical Lie Algebra for Many Fermion Green Functions

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概要

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• The Thermal Matsubara Green Functions, and their zero temperature analogs, in many-fermion systems are shown to be built up from products, or sums of products, of factors each of which is determined by a Lie Algebra. These factors are : the structure constants of a mapping φ of the B_<2N+1> Fermion Algebra (consisting of singles and pairs of fermion operators) onto itself ; and the structure constants of a mapping φ' of the D_<2N+1> Dynamical Algebra of the Hamiltonian (consisting of pairs of fermion operators) onto itself ; and eigenvalues of the generators of the Abelian Cartan subalgebra. Eigenstates of the many-fermion Hamiltonian typically relate to different types or numbers of elementary excitations (quasi-particles) ; these states are shown to be bases for irreducible representations of the Dynamical Algebra. The contribution of each such irreducible set of states to the Green Functions is exhibited. These results are exact for mean-field Hamiltonians ; generalization to include effects of fluctuations may be possible. The Green Functions for a model BCS singlet superconductor are determined (Dynamical Algebra SU (2)) to illustrate the various steps in the analysis.

• 理論物理学刊行会の論文
• 1985-03-31

著者

• Solomon Allan

  Department Of Theoretical Physics University Of Oxford : Faculty Of Mathematics Open University

• BIRMAN Joseph

  Department of Theoretical Physics, University of Oxford

• Birman Joseph

  Department Of Theoretical Physics University Of Oxford : Department. Of Physics City College Of The

• BIRMAN Joseph

  Department of Theoretical Physics, University of Oxford : Department. of Physics, City College of the City University of New York

関連論文

• Methods of Dynamical Lie Algebra for Many Fermion Green Functions

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