Progress of Theoretical Physics

Mori's Method and Feynman Diagram Method

Edson Sardella, A. F. S. Moreira

Published Nov 1, 1989• 1 citation

Abstract

Mori's method is applied to the Ginzburg-Landau Hamiltonian for a system of interacting spins. The Green's function and the self-energy obtained are very similar to those determined using a Feynman diagram method.

DOI: 10.1143/ptp.82.911

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Progress of Theoretical Physics

Mori's Method and Feynman Diagram Method

Edson Sardella, A. F. S. Moreira

Published Nov 1, 1989• 1 citation

Publisher

Abstract

DOI: 10.1143/ptp.82.911

Related papers

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Antonio S. T. Pires, M. E. Gouvêa

Brazilian Journal of PhysicsSep 1, 20045 citations

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P. Gluck

Proceedings of the Physical SocietySep 1, 19673 citations

On the Green Function of the Spin System. II

Kyozi Kawasaki, Hazime Mori

Progress of Theoretical Physics Vol. 28 No. 4 (1962) pp. 690-710 On the Green's Functions of the Heisenberg Spin Systems Kyozi Kawasaki and Hazime Mori

Progress of Theoretical PhysicsJun 1, 196111 citations

Interacting electrons. Green functions and Feynman diagrams (methods of field theory in many-particle physics)

Daniel I. Khomskii

Cambridge University Press eBooksSep 2, 20100 citations

Phenomenological application of the projection-operator method and its connection with critical dynamics

Edson Sardella

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Behnam Farid

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arXiv:1912.00474Dec 1, 20192 citations

On the basis of an exact perturbational expression for the interacting one-particle Green function

G

corresponding to bosons / fermions in terms of the bare interaction potential

v

and permanents / determinants of the non-interacting one-particle Green function

G_0

, we deduce four recursive perturbation expansions for the self-energy

Σ

. With

W

denoting the dynamic screened interaction potential, these perturbation expansions are identical to those of

Σ

in terms of (i) self-energy diagrams and

(v, G_0)

, (ii)

G

-skeleton self-energy diagrams and

(v, G)

, (iii)

W

-skeleton self-energy diagrams and

(W, G_0)

, and (iv)

G

- and

W

-skeleton self-energy diagrams and

(W,G)

. For the calculation of

W

, we rely on a similar exact perturbational expression for the interacting two-particle Green function

G_2

as for

G

. From this expression, we deduce four recursive perturbation expansions for the polarization function

P

, necessary for the calculation of

W

, that are similar to those for

Σ

specified above. The correlation functions considered in this paper may be corresponding to ground states, and thermal ensemble of states. For thermal ensemble of states, we consider both the imaginary-time formalism of Matsubara, and the real-time formalism of thermo-field dynamics (TFD). The latter is advantageous for the direct calculation of dynamic correlation functions. In an appendix, we apply the formalisms presented in this paper to the Hubbard Hamiltonian for spin-

\tfrac{1}{2}

fermions on a lattice in arbitrary

d

spatial dimensions. In two further appendices, we present methods and short programs for determining the

ν

th-order diagrams corresponding to the perturbation expansions of

G

in terms of

(v,G_0)

, and

Σ

in terms of

(v,G_0)

and

(v,G)

on the basis of the cycle decompositions of the elements of the symmetric group

S_{2ν}