Mandelstam representation for the ladder approximation of the Bethe-Salpeter formalism

1960 ◽  
Vol 17 (4) ◽  
pp. 535-546 ◽  
Author(s):  
G. Wanders
Keyword(s):  
Ladder Approximation ◽  
Mandelstam Representation

scholarly journals A note on failure of the ladder approximation to QCD

2006 ◽  
Vol 640 (4) ◽  
pp. 196-200 ◽  
Author(s):  
Hong-Shi Zong ◽  
Wei-Min Sun
Keyword(s):  
Ladder Approximation

GENERALIZED COOPER PAIRING IN SUPERCONDUCTORS

2007 ◽  
Vol 21 (21) ◽  
pp. 3657-3686 ◽  
Author(s):  
M. DE LLANO ◽  
J. F. ANNETT
Keyword(s):  
Center Of Mass ◽  
Power Series Expansion ◽  
Hard Core ◽  
Ladder Approximation ◽  
Common Element ◽  
Electron Interaction ◽  
Einstein Condensation ◽  
Cooper Pairing ◽  
Linear Dispersion ◽  
Energy Instability

We review Cooper pairing starting from its simplest, original 1956 version of two electrons interacting above the Fermi sea of an ideal Fermi gas (IFG). The two-electron interaction assumed extensively (if not exclusively), is the attractive two-parameter Cooper, and then BCS, model interactions. Hole Cooper pairs (CPs) and electron-hole CPs are then included along with the initial electron-CPs in terms of the single-fermion Green functions implied by the Bethe-Salpeter (BS) integral equation in the ladder approximation. A purely-imaginary CP energy "instability" is recovered that is well-documented in the literature at least since the late 1950's. A novel interpretation of this instability is that an unperturbed Hamiltonian different from the IFG one first used by Cooper suffices to obtain meaningful CPs. Instead of the IFG sea, a BCS-correlated Fermi "sea" used in the BS equation interpreted as the associated unperturbed Hamiltonian leads to real CP energies (with small imaginary terms implying damping). We survey how this has been achieved in 1D, 2D and 3D, and give a more detailed treatment in 2D. A vital distinction is that the original and generalized CPs are true bosons in contrast with BCS pairs that are not ordinary bosons but rather "hard-core bosons" as they do not obey strict Bose commutation rules. Another important common element of the original or generalized CPs (particularly in 2D where ordinary Bose-Einstein condensation (BEC) does not occur) is their linear dispersion relation in leading order in the total (or, center-of-mass) momentum power-series expansion of the CP energy. This theory encompasses, in principle, all empirically known superconductors including quasi-2D superconductors such as cuprates and the ET organic compounds, as well as quasi-1D ones such as the organometallic Bechgaard salts and nanotubes.

scholarly journals Gauge-invariant models for two-body scattering with the Bethe-Salpeter ladder approximation

1974 ◽  
Vol 10 (5) ◽  
pp. 1553-1560 ◽  
Author(s):  
Gerald E. Hite ◽  
Harald J. W. Müller-Kirsten
Keyword(s):  
Ladder Approximation ◽  
Gauge Invariant

scholarly journals Heavy-light mesons beyond the ladder approximation

2020 ◽  
Vol 101 (11) ◽  
Author(s):  
Pianpian Qin ◽  
Si-xue Qin ◽  
Yu-xin Liu
Keyword(s):  
Ladder Approximation ◽  
Light Mesons
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