arXiv:1108.0815

Ward Identities for Cooper Pairs

Osamu Narikiyo

Published Aug 3, 2011• 4 citations

Abstract

Ward identities for Cooper pairs are derived. These give consistent description of electronic curent vertex and thermal current vertex.

DOI: 10.48550/arxiv.1108.0815

Related papers

On the vertex function method in the Tomonaga-Luttinger model

Marian Apostol

The Ward identities relating the three-point vertex functions to the single-particle Green functions as well as the generalised Ward identities between the four- and three-point vertex functions are derived analytically for the Tomonaga-Luttinger model by using explicitly the boson algebra of the particle-hole operators.

Journal of Physics C Solid State PhysicsFeb 10, 19830 citations

Ward identity for non-relativistic fermions

Marian Apostol

Physics Letters AJul 1, 19803 citations

Ward identities for charge and heat currents of particle-particle and particle-hole pairs

Osamu Narikiyo

The Ward identities for the charge and heat currents are derived for particle-particle and particle-hole pairs. They are the exact constraints on the current-vertex functions imposed by conservation laws and should be satisfied by consistent theories. While the Ward identity for the charge current of electrons is well established, that for the heat current is not understood correctly. Thus the correct interpretation is presented. On this firm basis the Ward identities for pairs are discussed. As the application of the identity we criticize some inconsistent results in the studies of the superconducting fluctuation transport and the transport anomaly in the normal state of high- T c superconductors.

arXiv:1703.04409Europhysics Letters (EPL)Jul 1, 20141 citation

Exact commutation relations for the Cooper pair operators and the problem of two interacting Cooper’s pairs

Ilya G. Kaplan, Oracio Navarro, J.A. Sánchez

Physica C SuperconductivityDec 21, 20048 citations

Diagrammatic approach to the pairing instability in an interacting Fermi gas

Y. M. Malozovsky, Jiang-Di Fan

The pairing instability induced by either a given attractive interaction or particle-hole excitations is examined by using the perturbational diagram approach. A graphical functional derivative method based on Ward's identity is developed to represent the contributions to the interparticle interactions from different channels. It is shown that pairing instability for the electrons excited from the Fermi sea may happen due to the presence of holes even when the original interaction is repulsive. Thus, in contrast to the Cooper instability caused by a given attractive interaction, the pairing instability can be induced by the particle-hole excitations. The scattering diagrams from this model allows one to evaluate the two particle vertex function and Tc by using the pole condition of the vertex function. It has been found that Tc can reach quite high values and gives rise to the bell shape. The application of the results to a layered 2D Fermi gas is considered.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEJul 5, 19960 citations

Green functions in the renormalized many-body perturbation theory

V. Janiš

I review the way the many-body Green functions are used to renormalize the perturbation theory of correlated fermions. The Green functions are introduced to implement systematically dynamical corrections to the static mean-field theory. The renormalizations enter the perturbation theory via self-consistent evaluations of one-particle and two-particle Green functions. The one-particle self-consistency is discussed within the Baym-Kadanoff construction. We point to an inherent dichotomy of the Baym-Kadanoff approach in the relation between one and two-particle Green functions. They are the Schwinger-Dyson equation, directly derived from the generating Luttinger-Ward functional, and the Ward identity. The latter imposes a severe restriction on the two-particle irreducible vertex and is not guaranteed in the Baym-Kadanoff approach. No approximate theory is capable to obey both relations. I further discuss the two-particle approach with two-particle renormalizations that offers a way to reconcile the Schwinger-Dyson equation and the Ward identity. The two-particle irreducible vertex from the critical Bethe-Salpeter equation becomes a generating functional in the two-particle renormalization of the perturbation theory. The irreducible vertex is used in the Ward identity to determine the order parameter beyond the critical point and in the Bethe-Salpeter equation representing the vertex of the Schwinger-Dyson equation to determine the spectral self-energy in such a way that the thermodynamic critical behavior from both equations is qualitatively the same. Finally, I discuss a static mean-field-like approximation with a renormalized effective interaction determined self-consistently that leads to a qualitatively correct description of strong electron correlations in impurity and lattice models.

arXiv:2109.04231Sep 9, 20210 citations