In the usual theory of the two-time Green's function, decoupling techniques are introduced in order to obtain a self-closed equation for the lowest order Green's function. These decouplings give neither the correct temperature dependence (the absence of a ${T}^{3}$ term) of magnetization nor the correct correlation function $〈{{S}_{j}}^{\ensuremath{-}}{{S}_{j}}^{\ensuremath{-}}{{S}_{k}}^{+}{{S}_{l}}^{+}〉$, which should be zero by definition. In this paper the equation of motion for the higher order Green's function is solved in the approximation which will lead to correct results up to terms of order ${T}^{3}$ in these quantities. Employing this higher order Green's function, it is found that the correction to the magnetization consists of a term of order ${T}^{4}$ and a divergent term and that the correlation function consists of a term of order ${T}^{3}$ and a divergent term. A method extracting a significant part from this divergent term is found by analyzing a system of two interacting \textonehalf{} spins. By this method, it is shown that the ${T}^{3}$ term in the magnetization is completely eliminated and that the correlation function $〈{{S}_{j}}^{\ensuremath{-}}{{S}_{j}}^{\ensuremath{-}}{{S}_{k}}^{+}{{S}_{l}}^{+}〉$ vanishes identically.In the usual theory of the two-time Green's function, decoupling techniques are introduced in order to obtain a self-closed equation for the lowest order Green's function. These decouplings give neither the correct temperature dependence (the absence of a ${T}^{3}$ term) of magnetization nor the correct correlation function $〈{{S}_{j}}^{\ensuremath{-}}{{S}_{j}}^{\ensuremath{-}}{{S}_{k}}^{+}{{S}_{l}}^{+}〉$, which should be zero by definition. In this paper the equation of motion for the higher order Green's function is solved in the approximation which will lead to correct results up to terms of order ${T}^{3}$ in these quantities. Employing this higher order Green's function, it is found that the correction to the magnetization consists of a term of order ${T}^{4}$ and a divergent term and that the correlation function consists of a term of order ${T}^{3}$ and a divergent term. A method extracting a significant part from this divergent term is found by analyzing a system of two interacting \textonehalf{} spins. By this method, it is shown that the ${T}^{3}$ term in the magnetization is completely eliminated and that the correlation function $〈{{S}_{j}}^{\ensuremath{-}}{{S}_{j}}^{\ensuremath{-}}{{S}_{k}}^{+}{{S}_{l}}^{+}〉$ vanishes identically.

Physical ReviewJan 18, 196523 citations

First order green function theory of ferromagnetism II

Seiichiro Katsura, T. Horiguchi

Physics Letters ADec 1, 19685 citations

Perturbation Theory for Spin Green's Functions

D. I. Kadyrov

Soviet physics. DokladyJun 1, 19700 citations

Green’s Function Perspective on the Nonlinear Density Response of Quantum Many-Body Systems

Jan Vorberger, Tobias Dornheim, Maximilian Böhme +2 more

We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin-Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin-Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.

arXiv:2410.01845Journal of Statistical PhysicsMay 24, 20256 citations

Field-theoretical methods in quantum magnetism

D. C. Cabra, Pierre Pujol

Lecture notes in physicsJan 1, 200422 citations

Theory of spherically symmetric potentials†

Jagdish Chandra, R. P. Gairola, B. D. Indu

The interpretation as well as derivation of the multi‐dimensional wave functions for spherically symmetric potentials is an uphill task in quantum mechanics. The wave functions for spherical harmonics are obtained in the context of hydrogen‐like atoms using the theory of Green's functions. The process of obtaining the Green's functions is new and is being reported for the first time. The process elucidates all the relevant features whatsoever required by the system. One of the salient features of the technique used is that it reduces all the hierarchies and higher‐order Green's functions to Green's functions of the lowest order.The interpretation as well as derivation of the multi‐dimensional wave functions for spherically symmetric potentials is an uphill task in quantum mechanics. The wave functions for spherical harmonics are obtained in the context of hydrogen‐like atoms using the theory of Green's functions. The process of obtaining the Green's functions is new and is being reported for the first time. The process elucidates all the relevant features whatsoever required by the system. One of the salient features of the technique used is that it reduces all the hierarchies and higher‐order Green's functions to Green's functions of the lowest order.

International Journal of Mathematical Education in Science and TechnologyJul 1, 19830 citations

{T}^{3}

term) of magnetization nor the correct correlation function $〈{{S}_{j}}^{\ensuremath{-}}{{S}_{j}}^{\ensuremath{-}}{{S}_{k}}^{+}{{S}_{l}}^{+}〉$, which should be zero by definition. In this paper the equation of motion for the higher order Green's function is solved in the approximation which will lead to correct results up to terms of order

{T}^{3}

in these quantities. Employing this higher order Green's function, it is found that the correction to the magnetization consists of a term of order

{T}^{4}

and a divergent term and that the correlation function consists of a term of order

{T}^{3}

and a divergent term. A method extracting a significant part from this divergent term is found by analyzing a system of two interacting \textonehalf{} spins. By this method, it is shown that the

{T}^{3}

term in the magnetization is completely eliminated and that the correlation function $〈{{S}_{j}}^{\ensuremath{-}}{{S}_{j}}^{\ensuremath{-}}{{S}_{k}}^{+}{{S}_{l}}^{+}〉$ vanishes identically.