The algebraic diagrammatic construction scheme at nth order includes all Feynman diagrams up to nth order and a partial summation of diagrams arising from the latter to infinite order. In the present work this scheme is carried out for the first time at third order for the particle-particle propagator. Because of the many diagrams involved in third order the approach requires a very careful analysis of terms which describe the corresponding perturbation expansion of the propagator. The relevant technical details of the analysis are presented.The algebraic diagrammatic construction scheme at nth order includes all Feynman diagrams up to nth order and a partial summation of diagrams arising from the latter to infinite order. In the present work this scheme is carried out for the first time at third order for the particle-particle propagator. Because of the many diagrams involved in third order the approach requires a very careful analysis of terms which describe the corresponding perturbation expansion of the propagator. The relevant technical details of the analysis are presented.

Physical Review AFeb 1, 198960 citations

SO(3) Algebra and the Conservation of Helicity in the First Order Aharonov-Bohm Scattering Amplitude

A. Albeed, M. S. Shikakhwa

For a Dirac particle in an Aharonov-Bohm (AB) potential, it is shown that the spin interaction (SI) operator which governs the transitions in the spin sector of the first order S-matrix closes the SO(3) algebra with other two operators in the spin space of the particle. Expressing the helicity operators of the incident and scattered particles in terms of these new generators, conservation of helicity in the transition is established algebraically as a consequence of this algebra at the operator level in a simple and transparent manner. The case of a non-relativistic spin-1/2 particle is also discussed along similar lines.For a Dirac particle in an Aharonov-Bohm (AB) potential, it is shown that the spin interaction (SI) operator which governs the transitions in the spin sector of the first order S-matrix closes the SO(3) algebra with other two operators in the spin space of the particle. Expressing the helicity operators of the incident and scattered particles in terms of these new generators, conservation of helicity in the transition is established algebraically as a consequence of this algebra at the operator level in a simple and transparent manner. The case of a non-relativistic spin-1/2 particle is also discussed along similar lines.

Aug 11, 20040 citations

Particles with Spin

Siegfried Flügge

Springer eBooksJan 1, 19991 citation

Particles with Spin

Springer eBooksNov 13, 20050 citations

New approach to the one-particle Green's function for finite Fermi systems

J. Schirmer, Lorenz S. Cederbaum, Olaf Walter

A new approach to the one-particle Green's functions $\mathit{G}$ for finite electronic systems is presented. This approach is based on the diagrammatic perturbation expansions of the Green's function and of the dynamic self-energy part $\mathit{M}$ related to $\mathit{G}$ via the Dyson equation. The exact summation of the latter expansion is reformulated in terms of a simple algebraic form referred to as algebraic diagrammatic construction (ADC). The ADC defines in a systematical way a set of approximation schemes ( $n\mathrm{th}$ -order ADC schemes) that represent infinite partial summations for $\mathit{M}$ and (via the Dyson equation) for $\mathit{G}$ being complete through $n\mathrm{th}$ order of perturbation theory. The corresponding mathematical procedures are essentially Hermitian eigenvalue problems in restricted configuration spaces of unperturbed ionic configurations. Explicit equations for the second-, third-, and fourth-order ADC schemes are derived and analyzed. While the second- and third-order schemes can be viewed as systematic rederivations of previous approximation schemes, the fourth-order ADC scheme represents a complete fourth-order approximation for the self-energy and the one-particle Green's function which was hitherto not available.A new approach to the one-particle Green's functions $\mathit{G}$ for finite electronic systems is presented. This approach is based on the diagrammatic perturbation expansions of the Green's function and of the dynamic self-energy part $\mathit{M}$ related to $\mathit{G}$ via the Dyson equation. The exact summation of the latter expansion is reformulated in terms of a simple algebraic form referred to as algebraic diagrammatic construction (ADC). The ADC defines in a systematical way a set of approximation schemes ($n\mathrm{th}$-order ADC schemes) that represent infinite partial summations for $\mathit{M}$ and (via the Dyson equation) for $\mathit{G}$ being complete through $n\mathrm{th}$ order of perturbation theory. The corresponding mathematical procedures are essentially Hermitian eigenvalue problems in restricted configuration spaces of unperturbed ionic configurations. Explicit equations for the second-, third-, and fourth-order ADC schemes are derived and analyzed. While the second- and third-order schemes can be viewed as systematic rederivations of previous approximation schemes, the fourth-order ADC scheme represents a complete fourth-order approximation for the self-energy and the one-particle Green's function which was hitherto not available.

Physical Review ASep 1, 1983725 citations

A new approach to the one-particle Green's functions

\mathit{G}

for finite electronic systems is presented. This approach is based on the diagrammatic perturbation expansions of the Green's function and of the dynamic self-energy part

\mathit{M}

related to

\mathit{G}

via the Dyson equation. The exact summation of the latter expansion is reformulated in terms of a simple algebraic form referred to as algebraic diagrammatic construction (ADC). The ADC defines in a systematical way a set of approximation schemes (

n\mathrm{th}

-order ADC schemes) that represent infinite partial summations for

\mathit{M}

and (via the Dyson equation) for

\mathit{G}

being complete through

n\mathrm{th}

order of perturbation theory. The corresponding mathematical procedures are essentially Hermitian eigenvalue problems in restricted configuration spaces of unperturbed ionic configurations. Explicit equations for the second-, third-, and fourth-order ADC schemes are derived and analyzed. While the second- and third-order schemes can be viewed as systematic rederivations of previous approximation schemes, the fourth-order ADC scheme represents a complete fourth-order approximation for the self-energy and the one-particle Green's function which was hitherto not available.